temperature measurements in hypervelocity flows using

Temperature Measurements in Hypervelocity Flowsusing Thermally-Assisted Laser-Induced Fluorescence

Tamara SopekMSc (Aerospace Engineering), MEng (Aeronautical Engineering)

A thesis submitted for the degree of Doctor of Philosophy atThe University of Queensland in 2017

School of Mechanical and Mining EngineeringCentre for Hypersonics

Abstract

Scramjet engines with their very high specific impulse have the potential to outperform rocket motorsas a means of propelling hypersonic vehicles. The scope of this project is to determine temperaturesin the scramjet combustor using an advanced optical diagnostic technique, namely laser-induced flu-orescence. Presently, direct temperature measurements are not readily available for scramjets, due tothree reasons. Firstly, commonly-used gauges for temperature measurements, such as thermocouplesand heat transfer gauges would not survive or would be damaged at the extreme temperatures typicallyoccurring in scramjets (around T = 1100 - 2500 K), and therefore these gauges would not give accuratereadings. Secondly, measurements with any gauges would be intrusive, and their presence in the flowmight cause large disturbances. Thirdly, these gauges can only provide discrete, point measurements.Laser-induced fluorescence measurements present an optical non-intrusive technique to resolve tem-peratures in the combustor. Additionally, LIF measurements allow the temperatures in the combustorto be resolved at a higher spatial resolution than regular gauges. The new contribution made by thisPhD project is the application of a sophisticated optical diagnostic technique, thermally-assisted laser-induced fluorescence, to the temperature measurements in the combustor of a supersonic combustionengine. The issues with the technique and the way it should be used for application to scramjet flowswere explored. This required the development of the new knowledge and understanding of the spec-troscopy that underpins the technique. The project is significant because, to the author’s knowledge,this is the first time thermally-assisted LIF has been used for scramjet flows in a test facility. Cur-rently available thermometry methods usually require averaged repeated experiments, thus causinghigh cost of experiments. This study represents successful single-shot scramjet temperature measure-ments. The project was approached theoretically (synthetic spectra), experimentally and numerically(CFD and LIF modelling).

Radiation simulation programs providing synthetic OH spectra represent the theoretical part of thisstudy, as they employ theoretical expressions for spectral calculations. The OH radical is an inter-mediate species in the combustion, created in high quantities, therefore allowing direct fluorescencemeasurements. In this work, three numerical codes were used - LIFBASE, SPARTAN and Photaura.SPARTAN and Photaura were modified in order to include the OH molecule. The results presentedhere show that OH spectra produced using these programs show very good agreement. All threeprograms give correct and reliable representation of the physical phenomena in the wavelength rangestudied.

Experimental data was obtained through laser-induced fluorescence with a laser beam focused intothe combustor exciting an OH molecule transition. The experiments were conducted in the T4 shocktunnel using a scramjet model. LIF measurements were performed to resolve temperatures in thecombustor.

The numerical aspect presented in the project are the results of Bricalli (2015), in the form of thecomputational fluid dynamics (CFD) simulations of the combustion process, which provided the indi-cation of the phenomena occurring in the flow studied. Additionally, these results presented a valuablecomparison to experimental temperature distribution.

Detailed numerical modelling which simulates all radiative and collisional processes of relevance withthe appropriate system of differential equations is required to accurately calculate the total molecularconcentration and temperature from the observed fluorescence signal. Such numerical modelling,especially for the unsteady-state case, requires accurate knowledge on electronic quenching as wellas information on vibrational and rotational energy transfer. Calculations of this type are necessaryfor analysis of the influence of energy transfer processes on the fluorescence signal. Thus, a detailednumerical model was developed for purpose of such analysis.

The results of all aspects of the project were compared to deduce the accuracy and reliability of theexperimental results and the experimental technique. Comparison of the experimental spectra with thethree synthetic spectra showed that the OH concentrations were only partially thermalised. Therefore,non-equilibrium spectral simulations had to be used. By evaluating the scramjet LIF spectra with afull spectral fit, a temperature distribution across the combustor width was obtained. The comparisonof this temperature distribution with the CFD results showed a reasonable agreement between the ex-periments and CFD for one side of the scramjet, while the other side showed a significant discrepancybetween the data. As both LIF and pressure experimental data indicated combustion in this region,while the CFD results showed no combustion occurrence, the CFD results were found to be an inad-equate representation of the combustion in the used scramjet. The population distributions achievedwith numerical modelling of the LIF process validated the approach used to deduce temperatures.

This study produced a novel method for temperatures measurements in the scramjet combustor. Theavailability of a thermometry technique that provides temperature from a single run of a test facility isespecially appealing considering the significant per-shot cost of running high enthalpy facilities. Theoutcome of the project brings new resources which can be further used in advancing the technologyof operational scramjet engines for hypersonic vehicles.

Declaration By Author

This thesis is composed of my original work, and contains no material previously published or writtenby another person except where due reference has been made in the text. I have clearly stated thecontribution by others to jointly-authored works that I have included in my thesis.

I have clearly stated the contribution of others to my thesis as a whole, including statistical assistance,survey design, data analysis, significant technical procedures, professional editorial advice, and anyother original research work used or reported in my thesis. The content of my thesis is the result ofwork I have carried out since the commencement of my research higher degree candidature and doesnot include a substantial part of work that has been submitted to qualify for the award of any otherdegree or diploma in any university or other tertiary institution. I have clearly stated which parts ofmy thesis, if any, have been submitted to qualify for another award.

I acknowledge that an electronic copy of my thesis must be lodged with the University Library and,subject to the policy and procedures of The University of Queensland, the thesis be made availablefor research and study in accordance with the Copyright Act 1968 unless a period of embargo hasbeen approved by the Dean of the Graduate School.

I acknowledge that copyright of all material contained in my thesis resides with the copyright holder(s)of that material. Where appropriate I have obtained copyright permission from the copyright holderto reproduce material in this thesis.

Publications during candidature

Vanyai, T., Bricalli, M., Sopek, T., Brieschenk, S., McIntyre, T., Boyce, R.

“An Experimental Investigation of a Thermal Compression Scramjet with OH Imaging”, 20thAIAA International Space Planes and Hypersonic Systems and Technologies Conference,Glasgow, Scotland, 6 - 9 July 2015

Sopek, T., Brieschenk, S., Lorrain, P., McIntyre, T., Boyce, R.

“Code development to determine the temperature from the OH* chemiluminescence recordingsin a supersonic combusting flow”, AIAA International Space Planes and Hypersonic Systemsand Technologies Conference, Atlanta, GA, United States, 16 - 20 June 2014

Publications included in this thesis

Sopek, T., Brieschenk, S., Lorrain, P., McIntyre, T., Boyce, R.

“Code development to determine the temperature from the OH* chemiluminescence recordingsin a supersonic combusting flow”, AIAA International Space Planes and Hypersonic Systemsand Technologies Conference, Atlanta, GA, United States, 16 - 20 June 2014 - incorporated asChapter 3.

Contributor Statement of contribution

Sopek, T. (Candidate) Performed analysis (90%)Wrote the paper (100%)

Brieschenk, S. Performed experiments (30%)Performed analysis (10%)Edited paper (20%)

Lorrain, P. Designed experiments (30%)Performed experiments (70%)

McIntyre, T. Edited paper (70%)Boyce, R. Designed experiments (70%)

Edited paper (10%)

Statement of contributions by others to the thesis

Funding for this research project was provided by Prof. Russell R. Boyce.

The establishment of the new LIF capability in T4 facility was done together with Dr. Stefan Bri-eschenk and Tristan Vanyai, as well as the preparation of the experiments.

Tristan Vanyai and Dr. Wilson Chan provided assistance with performing the experiments.

A/Prof. Tim McIntyre and Dr. Bianca Capra provided critical review of this research.

Statement of parts of the thesis submitted to qualify for the award of another degree

None

Acknowledgments

The last couple of years have been exceptionally busy, challenging, hectic, but also exciting andrewarding. There is a large group of people that I would like to thank for their support during thistime. First of all, my primary supervisor, A/Prof. Tim McIntyre, for constant guidance, support andadvice during my PhD studies. Thank you for sharing your knowledge, for many helpful insights intoimproving this project along the way, and for always finding the time for me.

To my supervisor, Dr. Stefan Brieschenk, for his assistance, support and encouragement in realisationof this research. Also, for sharing his enthusiasm for research and optics.

Many thanks go to my supervisor Prof. Richard Morgan, who stepped in from the second year of mycandidature, and for his guidance during these years.

A great deal of appreciation is owed to Prof. Russell Boyce, who took me in as a PhD student,provided funding for this research and also for his help and advice during his time as my primarysupervisor.

Special thanks go to Prof. Ron Hanson, for giving me the opportunity to join his group at Stanford,and to learn the Stanford way of doing research and optics.

I want to thank Dr. Bianca Capra for her support and encouragement, and also for reviewing thisthesis.

Thanks to our technician, Keith Hitchcock, for his technical experience, and his help with all thingsT4 related.

To Tristan Vanyai, for sharing the burden of establishing a new facility in T4 shock tunnel and inpreparation and running of the experiments.

Thanks to Kevin Basore, Will Landsberg and Zachary Denman for operating T4 facility during myexperiments.

I would also like to thank the rest of our Centre for Hypersonics group, for without them it wouldn’tbe the same experience.

Thanks to my friends who have supported me from afar, especially Zrinka and Andreja.

Many thanks go to my family for their love and support, during my whole life. They have been andalways will be there for me and I couldn’t be more grateful to them.

My little Bubbles, thank you for your cuddles and company, especially during the writing of thisthesis. It helped my spirit just having you around.

At last, greatest thanks go to Wilson, for all the ways he supported and helped me during these years.Words cannot express how much I am grateful for your presence in my life and for all your love.

Thanks to the University of Queensland and the Australian Space Research Program project Scramjet-based access-to-space systems (Scramspace) for funding this research.

Keywords

laser-induced, fluorescence, thermometry, optics, hypersonics, scramjet, shock tunnel, supersoniccombustion, air-breathing propulsion, experimental

Australian and New Zealand Standard Research Classifications (ANZSRC)

ANZSRC code: 090107, Hypersonic Propulsion and Hypersonic Aerodynamics, 50%ANZSRC code: 020503, Nonlinear optics and spectroscopy, 50%

Field of Research (FoR) Classification

FoR code: 0901, Aerospace Engineering, 50%FoR code: 0205, Optical Physics, 50%

Contents

List of Figures xvii

List of Tables xix

Nomenclature xxv

1 Introduction 1

2 Literature Review 6

2.1 Laser-induced fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Collision dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.1.2 Interferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 LIF Thermometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Thermally-assisted laser-fluorescence thermometry . . . . . . . . . . . . . . 21

3 Spectral Modelling 26

3.1 OH modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1.1 SPARTAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.1.2 Photaura . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.1.3 Comparison of SPARTAN, LIFBASE and Photaura synthetic spectra . . . . . 33

3.2 T4 shock tunnel experiments of Lorrain . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4 Experimental Approach 38

4.1 LIF system set-up in the T4 shock tunnel . . . . . . . . . . . . . . . . . . . . . . . . 38

4.1.1 Experimental Arrangement of the LIF system . . . . . . . . . . . . . . . . . 40

4.2 Scramjet model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.2.1 Model position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2.2 Scramjet Model Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2.3 Fuel injectors and supply system . . . . . . . . . . . . . . . . . . . . . . . . 46

4.3 Test conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4 Experimental Data Reduction: Test time and surface pressure . . . . . . . . . . . . . 50

4.4.1 Test time determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4.2 Surface pressure measurements . . . . . . . . . . . . . . . . . . . . . . . . 52

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5 Calibration of LIF setup 53

5.1 Flame experiments results and discussion . . . . . . . . . . . . . . . . . . . . . . . 56

5.1.1 Non-equilibrium spectral simulation . . . . . . . . . . . . . . . . . . . . . . 65

5.1.2 Multi-line thermometry: Boltzmann plot . . . . . . . . . . . . . . . . . . . 68

5.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6 Scramjet Combustion Experiments 78

6.1 OH LIF Thermometry Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.1.1 LIF results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

6.1.2 Non-equilibrium spectral simulation . . . . . . . . . . . . . . . . . . . . . . 88

6.2 OH Emission Spectroscopy Measurements . . . . . . . . . . . . . . . . . . . . . . . 97

6.3 OH PLIF imaging considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7 Modelling of the LIF process 107

7.1 Energy level models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.2 60-level rate equation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.2.1 Alternative case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

8 Conclusions and recommendations for future research 126

8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

8.2 Recommendations for Future Research . . . . . . . . . . . . . . . . . . . . . . . . . 131

Bibliography 133

Appendices 145

Appendix A Spectroscopic constants: OH-G.txt 145

Appendix B Spectroscopic constants: OH-LEV.txt 148

Appendix C Spectroscopic constants per vibrational level 149

Appendix D Rate model 152

D.1 Manifold 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

D.2 Manifold 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

D.3 Manifold 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

List of Figures

2.1 The excitation, relaxation and energy transfer processes of OH radicals. . . . . . . . 7

2.2 Thermally-assisted laser-induced fluorescence, adapted from Eckbreth (1996) . . . . 21

2.3 Energy-level diagram of the first electronic state of OH molecule, A2 Σ+, reproducedfrom Neuber et al. (1996). First three vibrational levels (v = 0, 1, 2) are shown. Thismodel takes into account only the vibrational energy transfer and quenching. . . . . . 24

2.4 Results from Neuber et al. (1996). a, open circles, variation of experimental meantemperature with the flame radius at the flame level x/D of flame with mass frac-tion H2 = 20%; solid curve, calculated mean temperature; filled circles, experimentalstandard deviation of the temperature caused by turbulent fluctuations; dashed curve,calculated standard deviation. b, fraction of spectra with high enough intensity for asuccessful evaluation 1in percentage2. c, open circles, experimental mean OH con-centration in molecules per volume, normalized to 100; solid curve, calculated meanOH concentration, normalized to 100; filled circles, experimental standard deviationof the OH concentration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1 Comparison of the OH spectra obtained using different programs. . . . . . . . . . . 34

3.2 Phtoaura: Intensity range from optically thin (∆L=1e−7 m), lowest intensity curve,to optically thick flow (∆L=1 m), highest intensity curve. Simulations done withT =3000 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Comparison of synthetic spectra with experimental results of Brieschenk et al. (2013);Lorrain (2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.1 Layout of the T4 free-piston shock tunnel (Doherty, 2013). . . . . . . . . . . . . . . 39

4.2 Optical set-up, LIF configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.3 Optical set-up, PLIF configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.4 Scramjet model used for current LIF thermometry experiments (Vanyai, 2017) . . . . 44

4.5 Isometric view of one half of the intake (Vanyai, 2017). . . . . . . . . . . . . . . . . 45

4.6 Numerical result for the thermal compression scramjet with φ=0.8 (Bricalli et al., 2012). 46

4.7 Schematic of the fuel delivery and injection system for T4 LIF experiments . . . . . 47

4.8 Fuel injection timing during a LIF experiment . . . . . . . . . . . . . . . . . . . . . 48

4.9 A time trace of the nozzle-supply pressure measured for test 11607. Flow establish-ment time and test time windows are indicated. . . . . . . . . . . . . . . . . . . . . 51

4.10 A time trace from a static pressure measurement taken in the vicinity of the axiallocation where LIF measurements were taken (test 11607). Flow establishment timeand test time windows are indicated. . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.1 Flame experiments setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2 PLIF images for Q1(8) at different positions in the flame, φ=0.3. . . . . . . . . . . . 54

5.3 Saturation curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.4 Flame experiments for Q1(8) at first laser position. . . . . . . . . . . . . . . . . . . 57

5.5 Flame experiments for Q1(8) at second laser position. . . . . . . . . . . . . . . . . . 58

5.6 Flame experiments for R2(13) at first laser position. . . . . . . . . . . . . . . . . . . 59

5.7 Flame experiments for R2(13) at second laser position. . . . . . . . . . . . . . . . . 60

5.8 Flame experiments for P1(2) at first laser position. . . . . . . . . . . . . . . . . . . . 61

5.9 Flame experiments for P1(2) at second laser position. . . . . . . . . . . . . . . . . . 62

5.10 Flame experiments for Q1(9) at first laser position. . . . . . . . . . . . . . . . . . . 63

5.11 Flame experiments for Q1(9) at second laser position. . . . . . . . . . . . . . . . . . 64

5.12 PLIF image for Q1(8) at first laser position, φ = 0.3 divided in sections. Sections arecounted from the bottom of the image towards the top. . . . . . . . . . . . . . . . . 65

5.13 Experimental spectrum fitted to LIFBASE spectrum. Spectra normalized to the samearea. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

5.14 Rotational population distribution for sec # 1, flame EXP1. . . . . . . . . . . . . . . 67

5.15 Coefficient of determination R2 for section # 1, flame EXP1. . . . . . . . . . . . . . 68

5.16 Temperature distribution in flame for EXP1. . . . . . . . . . . . . . . . . . . . . . . 69

5.17 Experimental spectrum fitted to LIFBASE spectrum.Spectra normalized to the samearea. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.18 Experimental spectrum fitted to LIFBASE spectrum. Spectra normalized to the samearea. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.19 Temperature distribution in flame for EXP5. . . . . . . . . . . . . . . . . . . . . . . 71

5.20 Comparison of temperature distributions in flame; position left. . . . . . . . . . . . . 75

5.21 Comparison of temperature distributions in flame; position middle. . . . . . . . . . . 76

6.1 Theoretical LIF OH spectrum at 1 atm and 3000 K. . . . . . . . . . . . . . . . . . . 79

6.2 Variation of the Q1(8) transition fluorescence signal with temperature, generated withLIFBASE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.3 Laser-induced fluorescence image. Sections in the image on the right are countedfrom the bottom of the image towards the top. . . . . . . . . . . . . . . . . . . . . . 80

6.4 Spatial intensity distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.5 Example of spectrum in a section. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.6 Spectra in all 10 sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.7 Relative standard deviation in all 10 sections for test # 11607. . . . . . . . . . . . . . 83

6.8 S/N ratio in all 10 sections for test # 11607. . . . . . . . . . . . . . . . . . . . . . . 83

6.9 Q1(8) excitation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6.10 Peak intensity ratio for different rotational lines for the test # 11607. . . . . . . . . . 86

6.11 Comparison of synthetic spectra with LIF for the same intensity ratio. LIF data ob-tained with Q1(8) laser-excitation. Normalized to the maximum intensity value. In-strumental broadening (apparatus function) set at 0.25 nm for all spectra. . . . . . . . 87

6.12 Experimental spectrum fitting to LIFBASE spectrum. Each LIFBASE spectrum is afit at different temperature value. All spectra normalized to the same area. . . . . . . 89

6.13 Scramjet experiment spectrum fitted to LIFBASE spectrum. Spectra normalized tothe same area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.14 Rotational population distribution for section # 2 test # 11607. . . . . . . . . . . . . . 90

6.15 Coefficient of determination R2 for section # 2 test # 11607. . . . . . . . . . . . . . . 91

6.16 Temperature distribution in thermal compression scramjet. . . . . . . . . . . . . . . 91

6.17 Comparison of temperature distribution in thermal compression scramjet for differenttests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

6.18 Example of spectra with low intensity signal. Spectra normalized to the same area.Sections with these spectra were excluded from the temperature distribution as tem-perature considered erroneous. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.19 Comparison of temperature distribution in thermal compression scramjet for differenttests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

6.20 Comparison of temperature distribution in thermal compression scramjet with CFD.The solid line shows Tav. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6.21 Pressure data for LIF tests. From the top: low compression, centre and high compres-sion region of the combustor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

6.22 Example of emission spectra for the whole image. . . . . . . . . . . . . . . . . . . . 97

6.23 Example of emission spectrum in a section. . . . . . . . . . . . . . . . . . . . . . . 97

6.24 Emission spectra in all 10 sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.25 Comparison of synthetic spectra at 3000 K with experimental results for the whole area. 99

6.26 Comparison of synthetic spectrum at 3000 K with experimental results for a section. . 99

6.27 Comparison of experimental results for one section with synthetic spectra for differentpath lengths ∆ L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.28 LIF image at 360 nm, for Q1(8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.29 LIF images at 360 nm, for different excitation lines. . . . . . . . . . . . . . . . . . . 102

6.30 LIF images at 360 nm, for Q1(8) and nitrogen as test gas. . . . . . . . . . . . . . . . 103

6.31 PLIF images for different excitation lines. . . . . . . . . . . . . . . . . . . . . . . . 104

6.32 LIF spectrum at 360 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.1 Two energy level diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

7.2 Four energy level model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

7.3 Five energy level model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.4 Example of population evolution in levels 1 and 2 for ∆ t = 300 ns. . . . . . . . . . . 116

7.5 Example of population evolution in levels of manifold 3 for ∆ t = 300 ns. . . . . . . . 118

7.6 Example of population evolution in levels of manifold 5 for ∆ t = 300 ns. . . . . . . . 119

7.7 Example of rotational distribution in vibrational levels v′ = 0, 1 and v′′ = 0 for ∆ t = 300 ns.120

7.8 Comparison of scramjet experiment and rate model spectra for different temperatures.Spectra normalized to the same area. . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.9 Comparison of scramjet experiment and rate model spectra for different R. Spectranormalized to the same area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.10 Comparison of scramjet experiment and rate model spectra for different V (1→0).Spectra normalized to the same area. . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.11 Comparison of scramjet experiment and rate model spectra for different Q. Spectranormalized to the same area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.12 Comparison of scramjet experiment and rate model spectra for different V (0→1).Spectra normalized to the same area. . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.13 Comparison of scramjet experiment and rate model spectra. Spectra normalized tothe same area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.14 Comparison of scramjet experiment and rate model spectra. Spectra normalized tothe same area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

D.1 Example of population evolution in levels of manifold 3 for ∆ t = 300 ns. . . . . . . . 153


D.3 Example of population evolution in levels of manifold 3 for ∆ t = 300 ns. Level 2 islevel 8 in the v′ = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155






D.9 Example of population evolution in levels of manifold 4 for ∆ t = 300 ns. Level 1 islevel 8 in the v = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161









List of Tables

3.1 Database.txt file particular species line. . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Inputs.txt file particular species line. . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.3 Guinterface.txt file particular species line. . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Vibrationally-specific variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.5 OH-LEV.txt file electronic level data. . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6 radiator_ library.py file particular species line. . . . . . . . . . . . . . . . . . . . . . 32

3.7 OH-radiators.py file particular species line. . . . . . . . . . . . . . . . . . . . . . . 32

3.8 OH.py file particular species line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.9 Input parameters in spectral simulations. . . . . . . . . . . . . . . . . . . . . . . . . 33

3.10 Flow conditions in experiments of Lorrain et al. (2014). . . . . . . . . . . . . . . . . 34

4.1 Nominal shock tunnel filling conditions. . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 Nozzle-supply conditions (subscript s) and test conditions at the exit of the nozzle(subscript ∞). The estimated species mass fractions X at the nozzle exit plane are alsoshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.1 Flame experiments. Laser position 1 (LP1) is at the left side of the flame, while laserposition 2 (LP2) is through the middle of the flame. . . . . . . . . . . . . . . . . . . 55

5.2 Parameters of spectral lines used for the OH multi-line thermometry experiments. . . 73

6.1 SN ratios for several different numbers of sections of a LIF image. . . . . . . . . . . 81

6.2 Iron (Fe I) energy levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.1 Comparison of total transfer rate constants. . . . . . . . . . . . . . . . . . . . . . . 114

7.2 Comparison of level transfer rate constants. . . . . . . . . . . . . . . . . . . . . . . 117

C.1 Vibrationally-specific constants [cm−1] for the X2Π ground level in LIFBASE. . . . 150

C.2 Vibrationally-specific constants [cm−1] for the A2Σ excited level in LIFBASE. . . . 151

Nomenclature

Acronyms

ANZSRC Australian and New Zealand Standard Research Classifications

CARS Coherent anti-Stokes Raman scattering

CFD Computational Fluid Dynamics

DFWM Degenerate four-wave mixing

ESTCj Equilibrium Shock Tube Code junior

FoR Field of Research

FWHM Full width at half maximum

ICCD Intensified Charged Coupled Device

LIF Laser-induced fluorescence

LITA Laser-induced thermal acoustics

LSF Laser saturated fluorescence

ODE Ordinary Differential Equation

PLIF Planar laser-induced fluorescence

ppm Parts per million

RET Rotational energy transfer

SN Signal-to-noise ratio

THAF Thermally-assisted fluorescence

UV Ultraviolet

VET Vibrational energy transfer

Greek Symbols

α Rotation-vibration interaction constant cm−1

∆ Difference -

∆ Uncertainty -

ηD Dissociation energy cm−1

ηI Ionization energy cm−1

ηopt Quantum efficiency of optical system (detector and optics) -

γ Spin-rotation constant cm−1

γJ Second spin-rotation constant cm−1

γJJ Third spin-rotation constant cm−1

κ Absorption coefficient m−1

Λ Quantum number of total electronic orbital angularmomentum along internuclear axis -

ν Frequency Hz

ν0 Centre frequency of transition s−1

ν0 Electronic energy of the excited molecule cm−1

Ω Collection solid angle sr

Ω/4π Collection solid angle as a fraction of sphere -

∂ Partial derivative -

φ Fuel-air equivalence ratio -

ΦF Fluorescence yield -

Π Designation of ground electronic state of OH -

ρν Laser spectral energy density Jm−3Hz−1

Σ Designation of first excited electronic state of OH -

σ Standard deviation -

σi Standard deviation for section i -

τ Laser pulse length s

τ10% Contamination time ms

Roman Symbols

m Mass flow rate kgs−1

A Einstein coefficient for spontaneous absorption/emission s−1

A First electronically excited state -

A Spontaneous emission rate constant s−1

Av Spin-orbit coupling constant cm−1

B Einstein B coefficient for stimulated absorption/emission m3J−1s−2

Bv Rotational constant cm−1

B12 Einstein B coefficient for stimulated absorptionfrom energy state 1→ 2 m3J−1s−2

D0 Electronic level dissociation energy cm−1

Dv First centrifugal distortion constant cm−1

dx Flow path m

E Energy of transition cm−1

E Laser energy J

f Focal length m

fB Boltzmann fraction -

FJ Rotational energy cm−1

g Degeneracy -

ge Electronic level degeneracy -

gn Spectral overlap integral -

Gv Vibrational energy cm−1

H Specific enthalpy Jkg−1

h Altitude m

h f Specific formation enthalpy Jkg−1

hs Specific stagnation enthalpy Jkg−1

Hv Second centrifugal distortion constant cm−1

Iν Spectral irradiance per unit frequency interval Wm−2Hz−1

j Emission coefficient Wm−3sr−1

kB Boltzmann constant JK−1

l Length of the interaction volume in the beam direction m

Lv Third centrifugal distortion constant cm−1

Mv Fourth centrifugal distortion constant cm−1

Ma Mach number -

N Rotational quantum number without spin -

n Number density m−3

NT Total species population -

Ne Population of the excited level particle m−3

Ni Population of the initial level particle m−3

p First Λ-doubling constant cm−1

p Pressure Pa

pPitot Pitot pressure Pa

pplenum Fuel plenum pressure Pa

Q Quenching rate constant s−1

q Dynamic pressure Pa

q Second Λ-doubling constant cm−1

R Rotational transfer rate constant s−1

S Imaged fluorescence signal; number of detected photons -

Siav Signal intensity averaged for section i -

SJ′J′′ Hönl-London factor; rotational line strength factor -

T Downward rate constant s−1

T Temperature K

Te Electronic energy cm−1

tn T-estimator for a number of samples n -

u Flow velocity ms−1

V Vibrational transfer rate constant s−1

v Vibrational quantum number -

Vei Downward vibrational transfer rate constant s−1

Vie Upward vibrational transfer rate constant s−1

W Absorption or stimulated emission rate constant s−1

we Vibrational frequency cm−1

X Ground electronic state -

Z Charge number -

Ztot Total partition function -

Superscripts

′ Upper energy state

′′ Lower energy state

Subscripts

0 Initial

0 Stagnation property

∞ Freestream property

avg Average property

B Boltzmann

CT Compression tube property

f light Equivalent flight property

rot rotational

TOT Total property

vib vibrational

Chapter 1

Introduction

The onset of hypersonic flight dates back to the middle of the 20th century. Rockets, the most com-mon example of hypersonic vehicles, have been studied and developed since this time, to the extentthat there is little scope for further improvement in the efficiency. Science has to look elsewhere for amore efficient approach. High-speed air-breathing propulsion could present the solution for access-to-space vehicles and cruise vehicles for long-range flights. Supersonic combustion ramjets (scramjets)are a special class of hypersonic air-breathing engines, which, unlike the rockets with on-board oxi-diser, take in the surrounding air for the combustion, reducing thus the propulsion system weight, i.e.,increasing the possible payload weight. These engines have been studied since the early 1960s, how-ever, despite their conceptual simplicity, the practical issues related to achieving sustained hypersonicflight have not yet been resolved. Thus, scramjets have yet to become an efficient and cost-effectiveaccess-to-space propulsion system. One of the major issues that needs to be resolved is the productionof sufficient net thrust which would enable acceleration over a wide range of Mach numbers. In orderto improve the performance of scramjets, it is important to have as much information possible on thephysical processes and conditions inside these engines.

Since the onset of hypersonic flight, temperature measurements have remained as one of the difficul-ties to the successful understanding of hypersonic flows. Compared to the temperature measurementsin the ambient environment, hypersonic flow presents much more hostile environment for the exper-imental probes. Thermocouples and heat transfer gauges commonly used to measure temperaturewould not survive in this environment or would be severely damaged and give inaccurate readings.However, attempts have been made to use these probes in hypersonics flows. A “fine wire” total tem-perature probe has been constructed, calibrated, and used at hypersonic speeds (Vas, 1972) to surveythe shock layer of a 10 deg halfangle cone. Using the probe temperatures, the measured local Pitotpressure and wall static pressure, the local total temperature together with other physical characteris-tics of the shock layer were determined. A good agreement was found between the total temperatureprofile obtained by this method and the predicted profiles by the van Driest (thin boundary layer),Mayne and Rubin (numerical) methods.

Section 1.0 2

Nevertheless, due to mentioned difficulties of performing accurate measurements in these harsh flows,the majority of researchers resorted to non-intrusive experimental methods. It has been demonstratedby many investigators that a variety of non-intrusive techniques is available for measurements in hy-personic flows. Sandeman and Ebrahim (1977) showed that the spatially resolved hook technique canbe used for measuring the excitation temperature of the CrI 1 - eV level. This excitation temperature,when compared with theoretical calculations of the CO2 gas temperature, follows the calculated gastemperature very closely between the shock and the body and suggests that the chromium is in localthermodynamic equilibrium with the gas. Temperature measurements in the test section of a hyper-sonic gun tunnel using a modified line-reversal two-beam optical pyrometer have been performed byBrown-Edwards (1967). Rotational temperature and nitrogen number density were measured (Grischet al., 1993) in the shock wave/boundary layer interaction region in a low pressure hypersonic air flowusing a nonlinear optical technique named dual-line coherent anti-Stokes Raman scattering (CARS).Palma et al. (2000) performed planar laser-induced fluorescence (PLIF) thermometry over a flat platein a chemically and vibrationally frozen hypersonic boundary-layer to resolve the discrepancies be-tween experimental boundary-layer profile data and theoretical predictions at hypersonic conditions.PLIF technique was also applied to measure both the velocity and the rotational temperature in thecentral plane of the flow field around an axisymmetric model of planetary entry probe (Hruschkaet al., 2011). In the study of ignition enhancement for scramjet combustion McGuire (2007) uti-lized PLIF to obtain qualitative images of OH distribution in combustor region, showing that themole fraction of OH increases with increasing enthalpy (temperature), a result that is consistent withthe findings of the computational ignition delay study. Another laser-induced non-intrusive techniquecalled Laser-induced Thermal Acoustics (LITA) was used in experimental investigation in a Ma = 1.45chemically reacting H2/air free jet at a total temperature of 1320 K (Hell et al., 2012). Measurementswere also performed in a turbulent supersonic air/air free jet and subsonic standard flames. Withthis technique the speed of sound is measured directly, allowing derivation of the static temperaturefor known species concentrations, and additionally velocity measurements can be included with amodified setup.

These examples show that a non-intrusive approach in hypersonic flows has many advantages overcommonly used intrusive methods. The non-intrusive laser techniques especially have many appeal-ing attributes, and some of the most compelling ones are that they are not perturbing the gas flow,they can be tailored for the measurement of specific thermodynamic parameters and species, and theycan provide excellent spatial and temporal resolution for the detailed characterization of the com-plex three-dimensional and time-dependent aerodynamic flows (McKenzie, 1993). Methods such asRaman scattering, CARS, Degenerate Four-Wave Mixing (DFWM), laser-induced thermal acoustics(LITA) and the widely used method of laser-induced fluorescence (LIF) are some of the options toperform measurements in hypervelocity flows. The disadvantages of laser spectroscopic techniques

Chapter 1 Introduction 3

are that they can be complex and costly to implement, they require optical access that is not alwayseasily provided in testing facilities and test models, and they require operation and analysis by expertstrained in fields other than fluid dynamics.

There are several laser-based methods that provide measurements of detectable molecular speciescharacteristics. The intensities of transitions between energy states provide information on the pop-ulation distribution over those energy levels, from which temperature and concentrations can be ob-tained. The identification of specific transitions is achieved through their spectral location. All ofthese techniques share a number of common attributes, and most commonly used methods are Ramanscattering and laser-induced fluorescence (LIF). While both methods have a high spatial and temporalresolution and are non-intrusive in nature, there are some major differences. Raman scattering is uti-lized for major species present in combustion, but because of the signal strength it generally cannotdetect trace species. LIF, due to high cross sections for this process, is noticeably more sensitive com-pared to the Raman scattering methods, enabling the trace species concentration measurement. Thus,laser-induced fluorescence and Raman methods combined together provide a broad range of speciesto be studied. The electronic absorptions of species and radicals important in combustion chemistryis in the 200 - 600 nm range, a region easily accessed by a laser. LIF has the requirement for a suitableemission spectrum in the visible or ultraviolet, and thus is less generally applicable than Raman spec-troscopy or CARS. These methods can be used in larger wavelength range, but for detection of majorspecies only. For suitable species LIF is many orders of magnitude more sensitive. However, withthat sensitivity comes the major disadvantage of LIF: due to the finite radiative lifetime of the realexcited state, collisions of the excited molecule with the other species influence not only the spectraldistribution, but also the magnitude of the fluorescence signals.

Of candidate laser-based methods, laser-induced fluorescence has proven to be a particularly robustand sensitive technique, thus it was used in the present study. Laser-induced fluorescence is mostaccurately described as an absorption, and subsequent spontaneous emission (after a finite period oftime) from the excited multiple states, since the fluorescence observed may not be from the directlypumped state only. Due to collisions, vibrational energy transfer (VET) and/or rotational energytransfer (RET) can occur and result in energy distribution among states other than the laser-excitedstate. LIF is convenient in the environments where the pool of radical species, e.g., OH, CH, NH,CN, C2 and pollutants, e.g., NO, CO, often resides in the concentration range below 0.01 (100 ppm).Due to its capability to detect flame radical and pollutant species at the ppm or even sub-ppm levelLIF gained appreciable attention (Eckbreth, 1996). Around thirty or more combustion intermediatesconsisting of combinations of O, N, H, C and S, including the atoms, have been detected by LIF,many in flames (Crosley and Smith, 1983).

The application of LIF requires the existence of a relevant species which is spectroscopically simple,radiatively absorbing at wavelengths that are accessible by a laser, and thermodynamically coupled

Section 1.0 4

to the flow studied. Only a few molecules can be used for LIF diagnostics in the H2/air combustion.Oxygen (both molecular and atomic) is an excellent option for diagnostics in non-reacting flows orin lean flames. The downside is that it is consumed in stoichiometric or fuel rich flames. Also,it requires two-photon approach (two lasers) which makes it impractical for present purposes. Analternative molecule for LIF diagnostics both in the mixing and the reaction zones of flames is NO.The issue here is that artificial seeding of NO may be required, which could perturb the reactionchemistry. The OH molecule, a naturally occurring molecule in the reaction zone, is relatively stableand sufficiently abundant for LIF measurements (Quagliaroli et al., 1993). Also, it is an importantoxidant, appearing in a large number of the prominent flame chemical reactions (Aldén et al., 1982).The ubiquity of the hydroxyl radical (OH) in combustion environments has led to its use for markingreaction zones in combustion processes (to indicate the progress of combustion), for discerning flowstructures, and for determining temperature or the flow velocity. OH exhibits strong UV absorptionand high non-resonant fluorescence yield (Palmer and Hanson, 1995) and thus it was the moleculeprobed in this study.

The issue with the temperature measurements through commonly used thermometry methods is thatthey require a minimum of two lasers/two detectors (e.g. two-photon LIF) or two repeatable tests (e.g.two-line PLIF) and frequently averaging is done to get reliable measurements. This is not practicablenor economical when using a high enthalpy facility such as shock tunnel considering the significantper-shot cost of running these facilities. Thus, a single-shot approach is not only more accurate giventhe environment in which present measurements were performed (turbulent, supersonic combustion),but also more economical.

The objective of this study is to determine temperatures in high speed flows, with the application to ascramjet combustor.

This project aims to develop a technique for temperature measurements in hypervelocity flows, i.e.for single-shot scramjet temperature measurements. Thermally-assisted LIF thermometry is used forthe first time for scramjet experiments. This project investigates the issues with the technique and themeans to apply the technique to scramjet flows. Through coupling of the experimental technique withanalysis and CFD an excellent insight into the use of the technique is provided. The outcome of theproject will help to improve and make easier the approach to thermometry in a scramjet combustor,which can be further used in the operational scramjet engines, i.e., hypersonic vehicles and flows.

Chapter 2 contains review of literature relevant for this project. Modelling of the OH spectra ispresented in Chapter 3. Chapter 4 gives the description of the experimental facility, experimentalmodel and test flow conditions. Calibration of the new LIF setup in the T4 shock tunnel facility isgiven in Chapter 5. Results of the scramjet experiments of the project is presented in Chapter 6.Modelling of the LIF process, including all intermediate sub-processes is described in Chapter 7.

Chapter 1 Introduction 5

Chapter 8 provides key findings and conclusions of the performed research and proposes approachfor the future research.

Chapter 2

Literature Review

This chapter starts with an introduction to the laser-induced fluorescence technique. Work that hasbeen previously conducted with this technique is also reviewed. The chapter ends with a brief de-scription of the specific technique of LIF that will be implemented in the scope of this project.

2.1 Laser-induced fluorescence

Fluorescence is a spontaneous emission of radiation from an electronically excited state of a speciesof interest. This molecule could have been excited to an upper energy level in several ways, e.g., bycollisions with photons, electrons or molecules (chemically or thermally). Lasers, especially pulsedlasers, present undoubtedly the best apparatus to provide spatially, temporally and spectrally selectiveexcitation. To perform laser-induced fluorescence (LIF) experiment, a laser is tuned to a suitableresonant wavelength of the molecule of interest and excites a fraction of its population to the upperstate of a radiative transition. The resulting electronically excited states then radiate the absorbedenergy that is not lost to other relaxation paths, at all wavelengths that are allowed by the normalfluorescence spectrum of the excited state (Figure 2.1). The fluorescent emission is usually collectedat a right angle to the laser beam direction, and focused through a filter into a detector. Because areal excited state is created (in contrast to a virtual state as, for example, in Raman scattering), LIF isextremely sensitive and is thus suitable for the measurement of transient species such as the chemicalintermediates in combustion processes (Crosley and Smith, 1982).

Fluorescence that occurs at the same wavelength as the excitation, i.e., from the same energy levelsinvolved in the absorption, is called resonance fluorescence. In most cases however, the fluorescencechosen to be detected is at a wavelength different from that of the incident excitation. Mostly, butnot exclusively, fluorescence occurs at longer wavelengths termed Stokes shifted as the emissioninvolves new levels not originally involved in the absorption process. In order to avoid interferencesfrom spuriously scattered laser light or Mie scattering, experimental investigations typically considerspectrally shifted fluorescence.

Chapter 2 Literature Review 7

A2Σ+

X2Π

Q

0

1

1

0

0123N

VET RET

2

Figure 2.1: The excitation, relaxation and energy transfer processes of OH radicals.

There are several basic criteria which must be satisfied to perform quantitative fluorescence measure-ments on a given molecule (Eckbreth, 1996):

• the molecule must have a known emission spectrum

• the molecule must have an absorption wavelength which is accessible to a tunable laser source

• the rate of radiative decay of the excited state must be known

• excited state losses due to collisional deactivation, photoionization and/or predissociation haveto be accounted for

• the dependence of these rate constants on temperature has to be known or accounted for.

OH corresponds to these requirements, it is a very well characterized molecule with lot of data readilyavailable.

The first known one dimensional imaging of OH LIF in a flame was done by Aldén et al. (1982). Inthat experiment the laser was propagated as a beam, producing a 1D fluorescence profile. Spatial dis-tribution of the laser-induced OH fluorescence as a function of height above the burner was obtained.The first demonstration of a method of two dimensional imaging of LIF (PLIF) from the naturally oc-curring flame radical OH was performed by Dyer and Crosley (1982). The difference of PLIF, when

Section 2.1 Laser-induced fluorescence 8

compared to single-point fluorescence measurements (LIF), lies in the ability to visualize relativespecies distributions over an entire planar cross section of the flow field, making it thus also a morecomplex technique. PLIF has been used for hypersonic flow visualisation (Fox et al., 2001a,b; Gastonet al., 2002), visualisation of a scramjet combustor (McIntyre et al., 1997), thermometry (Palma et al.,2003, 1998; Sutton et al., 1993) and velocimetry (Danehy et al., 2001, 2003).

There are various possible sources of error when implementing laser-induced fluorescence. Excitedelectronic state may experience losses due to collisional deactivation, photoionization and/or pre-dissociation. In predissociation the chemical bond is broken at an energy which is lower than ex-pected. However, in many experiments, photoionization and predissociation can be neglected, andonly collision-induced losses must be taken into account. This is due to the fact that most of theexcited states are not predissociative, unless specifically chosen. Interferences from laser scattering,other radiating species or difficulties due to radiative trapping can also occur. Interpretation of themeasurements obtained using laser-based techniques may also strongly depend on facility character-istics, which, in the case of high-speed flows and of large-scale facilities may introduce significanterrors that cannot be corrected without a full knowledge of the local flow composition, velocity andtemperature. These facility-based characteristics may include the following: strong gradients in pres-sure, temperature, and concentration; high concentration of water vapour or other quenching species;Doppler shift of the absorption frequency; optically thick medium for both incident and emitted ra-diation; fluorescence trapping; spectral interference from other flow species; and metallic impuritiesdue to erosion of the facility walls. In particular, the large pressure and temperature gradients causeconsiderable fluorescence signal variations due to high collisional quenching rates, as well as lineDoppler broadening which changes the spectral overlap integral between the laser and the absorp-tion transition. As the indicated systematic errors are additive to the noise-induced uncertainty theirmagnitude must be estimated as part of the design of (P)LIF systems for quantitative imaging of OHdistributions (Quagliaroli et al., 1993).

An example of the influence that the interferences have on the fluorescence signal strength are theexperiments of Morley (1982). In this study the fluorescence signal was observed to be degraded bynoise from several sources:

• Rayleigh scattering from flame gases and Mie scattering from entrained particles

• Stray light from optical surfaces, etc.

• Flame luminescence

• Shot noise

• Pulse-to-pulse variation of laser

• Electrical interference


2.1.1 Collision dynamics

Battles and Hanson (1995) stated that, because typical molecular radiative rate constant are of theorder of 107 s−1, while typical rate constants for collisions causing a change in energy level are≥ 109 s−1, the most likely fate for an excited molecule is to undergo collisional transfer to someother level. The lifetime of the v′ = 0, 1 state of OH is long, approximately 10−6 s (Dimpfl and Kin-sey, 1979), relative to the typical intermolecular collision time in test facilities (around 10−9 s). Thus,many collisions can occur before fluorescence is emitted, thereby quenching the excited electronicstate significantly. Molecular collisions that occur under flame considerations, which include ab-sorption lineshape broadening, radiative trapping and collisional de-activation or quenching, can beespecially severe at elevated pressures.

Collisions experienced by the electronically excited state are usually separated into two categories(Crosley, 1981):

• quenching collisions, with rate constant Q, returns the probed molecule from the excited upperstate back to the lower state (mostly, but not exclusively to the ground state) non-radiatively sothat it does not fluoresce

• energy transfer collisions transferring the molecule into a different level within the electroni-cally excited state, followed by either further collisions or fluorescence. Following a collisionthere will be either a change in only the rotational level or a change in both the vibrationaland rotational levels. The energy transfer rate constants (rotational with rate constant R andvibrational with rate constant V ) are specific to the initial and final quantum states and they aresummed over all collision partners.

All collisions together influence both the magnitude (electronic quenching) and spectral form (RETand VET) of the fluorescence signals. These collisional processes for OH radical are also both tem-perature and rotational-level dependent, making quantitative interpretation of OH LIF measurementsextremely difficult. The electronic quenching and energy transfer are competing processes, and themagnitude of R and/or V relative to Q is the vital parameter here, with two limiting cases of thisrelation:

1. R, V » Q: the excited molecule will experience numerous energy transfer collisions prior toquenching. This will result in the broad distribution (possibly thermal-like) of the excited stateover its internal energy levels, while the resulting fluorescence spectrum will reflect this widedistribution.


2. Q » R, V : the initially excited molecules will largely be quenched before undergoing energytransfer. The resulting fluorescence spectrum will be dominated by large peaks correspondingto lines emitted from the directly pumped level. This situation is termed “arrested relaxation”or “frozen excitation”.

The ratio of quenching rate constant, Q, to radiative rate constant, A, determines the total fluorescenceyield, ΦF , i.e., the number of photons emitted per molecule initially excited by the laser. The effectivequantum yield on the other hand takes into account the effects of energy transfer when the fluores-cence from only a particular set of excited state levels is detected. The energy transfer within excitedstates often occurs quite rapidly and even vibrational energy transfer cross sections can be similar orin excess of gas kinetic values, such that V , R and Q are of the same magnitude.

Stepowski and Cottereau (1981) found that depopulation of the upper rotational level directly excitedby the laser results from a competition between electronic quenching to the ground state and RET tothe other upper rotational levels. As the delay increases, other lines appear indicating that more andmore rotational levels are populated by RET, and meanwhile the total fluorescence intensity decreasesbecause of electronic quenching. In addition, with the increase of the delay, the rotational populationdistribution in the upper states tends towards a Boltzmann distribution.

In a study by Zizak et al. (1981) they reported that very good agreement was found between the the-oretical prediction and the experimentally obtained rotational populations. This study confirmed thepossibility of using thermally-assisted fluorescence to determine temperature in combusting flows.They also warn that a major concern in laser-excited fluorescence experiments is the possibility thatradiatively excited atoms or molecules suffer quenching or mixing collisions between the levels dur-ing the laser pulse, hence, an understanding of the laser-excited fluorescence spectra of molecules inflames requires knowledge of the collisional coupling between the levels. In order to extract the tem-perature from relaxed molecular spectra, an understanding and modelling of rotational and vibrationalrelaxation is necessary.

Electronic quenching

As previously said, the major difficulty with the quantitative application of the laser-induced fluores-cence is that quenching of fluorescence occurs. The more quenching collisions that occur, the less thefluorescence which is detected, thus collisional quenching can significantly lower signal-to-noise ra-tios. The rate of quenching, and hence the factor relating the fluorescence signal to the concentration,depends on the local conditions.

Electronic quenching collisions are highly exoergic (release of energy) and are therefore usually as-sumed independent of the small amount of rotational energy contained in the electronically excited


species. For the OH molecules, however, this is not the case. Previous studies have shown rota-tional state dependence of the electronic quenching, with the quenching rate constant tending to de-crease with the increase of rotational state (Burris et al., 1991, 1988; Cleveland and Wiesenfeld, 1988;Copeland and Crosley, 1984; Jeffries et al., 1988; McDermid and Laudenslager, 1982). At higher ro-tational numbers (≥ N′ = 10) the quenching rate constant remains approximately invariable. McDer-mid and Laudenslager (1982) observed a significant decrease in the rotational level specific electronicquenching rate constants when the OH rotational energy increased. Copeland and Crosley (1984)reported that the rotational state-specific rate constants were measured for the electronic quenchingof the OH A2Σ+ (v′ = 0) state by several colliders using time-resolved laser-induced fluorescence andthat a significant decrease in the electronic quenching rate constant was observed as the amount ofrotational excitation in the OH is increased from N′ = 0 to N′ = 7. The decrease was found to begreater than 60% for the diatomics and greater than 20% for H2O and D2O. Cattolica and Mataga(1991) observed the general decrease in the quenching cross section with increasing temperature andwith higher rotational level. They conclude that contributions from VET to the overall de-excitationrate constant can be neglected for all species; contribution of the vibrational relaxation to the totalde-excitation rate constant from v′=1 is much less than 20%.

Studies done at higher temperatures have shown that electronic quenching rate constant also exhibitstemperature dependence, again quenching rate constant decreasing with the increase of temperature(Copeland and Crosley, 1986; Garland and Crosley, 1986; Jeffries et al., 1986; Paul, 1994; Paul et al.,1995; Smith and Crosley, 1986). There is little or no variation of the quenching rate constant withtemperature in the high temperature region.

The OH electronic quenching rate constant in quenching by a large number of colliders has shownboth the rotational and temperature dependence, its magnitude depending on the quenching gas. Thisbehaviour has been explained with a model involving the formation of a collision complex betweenthe OH molecule and its collision partner, governed by long-range attractive forces. The model wasfirst proposed by Lengel and Crosley (1975) and supported in works of numerous investigators. Theseattractive forces are highly anisotropic (orientation-dependent), mainly due to the orientational natureof the OH dipole moment. There are therefore regions (valleys) on the anisotropic attractive interac-tion surface; in the quenching collision a non-rotating OH approaches along these valleys. As increas-ing rotation is imparted to the OH, these valleys are averaged out, and the ability of the collision pairto capture one another is decreased. Once this averaging occurs, further increase of OH rotation failsto lower further the rate constant for electronic quenching. Thus, quenching cross section decreaseswith increasing collision velocity and when averaged over a thermal velocity distribution the crosssection will also decrease with increasing temperature.

Quenching of the excited state determines the overall fluorescence yield and its value is obviouslycrucial in relating the observed fluorescence signals to the desired concentrations. Crosley (1981)


states several ways of dealing with the problem of accounting for the quenching:

1. calculation of Q using previously measured or estimated bimolecular constants

2. calibration of the fluorescence signals and extrapolation of energy transfer rate constants

3. direct measurement of Q in situ

4. optical saturation

1) Calculation or estimation of quenching rate constantsAs there are many sources of these values, the opinion of Crosley (1981) is that the most reliablevalues arise from LIF experiments where a single level is initially excited and, under some conditions,even a rather crude estimation of the quenching rate constant can provide valuable information.

One example is Bechtel and Teets (1979) who performed first measurement of OH concentrationin atmospheric pressure flames using LIF. They determined number densities of the dominant colli-sion partners (N2, H2O, CO2, CO, O2, H2) at each CH4/air flame position using Raman scattering.They used these concentrations to calculate OH quenching rate constants at each flame position. Theabsolute OH concentration was determined by normalizing to laser absorption measurements in thepost-flame gases of atmospheric pressure flat-flame burners. The resulting OH concentration profileacross the flame was in good agreement with the theoretical predictions for this flame.

2) Calibration and extrapolation of energy transfer rate constantsMüller et al. (1978, 1980) developed a simple method that instead of absolute collision rate con-stants incorporates only their temperature dependence. By employing narrow bandwidth detector,only emission from the initially pumped level was observed. In this limiting condition almost everyvibrational or rotational relaxation from that level is an effective quenching collision. This leads tototal quench summation as

∑j(k j

q + k jvib + k j

rot) [M j]−→∑j

kgas kinetic [M j]

Since gas kinetic quenching rate constant scales as T 1/2 and at a given pressure [M j] ∝ T−1, thequenching rate constant varies from flame to flame as T−1/2. This method is mostly useful throughthe post-flame region where neither temperature nor the molecular composition of the collision envi-ronment is varying drastically. Near the reaction zone relative values of Q, R and V vary from onecollision partner to another, and a temperature dependence of these rate constants more complex thanT 1/2 may become noticeable over a larger temperature range.

3) Direct lifetime measurementsIt was found that under certain conditions it is possible to directly measure the quenching rate constant


of the laser-excited molecules in situ. The limitation of this method is the requirement that Q+A <

τ−1L , where τL is the laser pulse length. Therefore, this requirement limits the application of the

method only for low-pressure flames, and not for atmospheric flames. Stepowski and Cottereau (1979)applied this method to measurement of OH concentration in propane-oxygen flames at total pressuresof about 20 torr. They proposed a method that is alternative to the saturation approach to avoid thequenching dependence of the fluorescence intensity. If the pulse duration is very much shorter thanquenching, radiative, and pumping times, the absolute concentration can be obtained from the peakvalue n0 and known value of τL, and is independent of the quenching rate constant which neverthelesscan be obtained from the time-resolved fluorescence decay.

4) Saturated LIFMethod of saturated fluorescence was initially proposed by Piepmeier (1972), and subsequently ex-tended by Daily (1977) for LIF probing of combustion intermediates. In systems where temperature,composition and density vary with time, such as in turbulent combustion or detonations, the flow maynot be sufficiently characterized, thus quenching cannot be calculated or estimated with confidence.The saturation method avoids the need for knowledge of collisional environment composition by per-forming the experiments at high enough laser intensity that the signal level becomes independent ofquenching rate constant. Baronavski and McDonald (1977a,b) first observed saturation behaviourin flames for C2. Subsequently it has been studied experimentally for other species as well, and itbecame apparent that for quantitative diagnostics spatial and temporal profiles of the laser beam mustbe taken into account. It was explained previously in this chapter that there are two limiting cases inwhich the energy transfer can be treated simply, Q»R, V and R, V »Q. Due to some simplifying ap-proximations, such as the steady state assumption during laser pulse, it does not seem that saturationspectroscopy possesses inherent advantages with regard to accuracy. Thus, when possible, operationin non-saturation regime remains preferable.

Kotlar et al. (1980) developed a multi-level model for more accurate treatment of saturated LIF. Themodel, a solution of time-dependent rate equations, describes excited state energy transfer using previ-ously measured state-specific rate constants and includes ground-state energy transfer with estimatedrate constants. They studied the intermediate situation where Q∼R, V has been considered in anumerical model of the response of OH to laser excitation, under conditions approaching optical sat-uration and in a collision environment at 2000 K corresponding to the burnt gases of an atmosphericpressure methane-air flame. The goal of the study was to explore the applicability of simplified ap-proaches for OH and other species. It was shown that for OH the simplified two-level approximationis inadequate. Another finding was that the steady-state approximation is not fully valid for 10 nslaser pulses in atmospheric pressure flames. They also showed the importance of the ground levelenergy transfer.

Lucht et al. (1980) proposed the balanced cross-rate method for analysis of laser-saturated fluores-


cence (LSF) in fluorescence measurements. In this model, that is a modification of the four leveltreatment of Berg and Shackleford (1979), single upper and lower rotational levels are assumed to bedirectly coupled by the laser radiation. In the limit of strong laser pumping (saturated regime), levels1 and 2 reach steady state rapidly, tens of picoseconds. If total population of the two laser-coupledrotational levels is constant during the laser pulse, the total molecular population can be calculatedfrom the observed upper rotational level population using a two-level saturation model and Boltz-mann statistics. The model will give accurate results provided that the rotational relaxation rates inthe upper and lower sets of rotational levels are approximately equal. It has been used for reductionof OH LIF data in flames up to several atmospheres pressure (Carter et al., 1992).

Collisional quenching are a source of systematic error in most LIF measurements. The error may besevere when the radiative lifetime of the excited state is long, relative to the time between collisions,and when the composition of the collisional partners varies widely. However, when water vapour isa major species, corrections for collisional quenching may be simplified by neglecting the contribu-tion of other major species (Quagliaroli et al., 1993). This is due to the high collisional electronicquenching cross section of OH with H2O.

Energy transfer

While quenching alters the overall signal levels and total quantum yield for LIF, vibrational energytransfer (VET) and rotational energy transfer (RET) may distribute the energy among other excitedstates. To determine concentrations from the LIF measurements the value of the effective quantumyield is needed. Also, if the effective quantum yield varies with energy level within the excited state,the energy transfer can significantly alter the value of the temperature determined (Crosley, 1981).As temperature is further used to calculate the LIF concentration, erroneous values of T will leadto erroneous concentration results. Morley (1982) stated that the ultimate fate of an excited OHmolecule is to radiate or be collisionally quenched, but before either of this happens, it may undergovibrational or rotational transfers within the excited state. If the radiative and quenching rate constantsare the same for all the vibrational-rotational states likely to be populated, then these processes donot affect the total amount of fluorescence, although they will affect its spectral distribution. In thestudy by Köllner et al. (1990) the entire fluorescence bands were collected. They asserted that suchdetection schemes are favoured for temperature measurements because then even the OH radicals thathave undergone rotational or vibrational relaxation are still detected. Thus errors caused by different(level-specific) collisional efficiencies are avoided.

The conclusion based on numerous observations is that the majority of the molecular energy transfer isstate-specific. The first measurements of state-specific energy transfer were performed by Carrington(1959). Using an excitation of OH in post-flame region of acetylene-oxygen flame he observed anon-thermal rotational distribution and deduced a ratio of rotational energy transfer to quenching to


be 2.2. This experiment is important as it showed that the rapid quenching and the thermalisationdon’t occur in the case of OH and that the energy transfer must be considered on a detailed basis.

1) Rotational energy transfer (RET)

Numerous researchers and groups studied rotational energy transfer of electronically excited OH,mostly within the v′ = 0 level (Burris et al., 1991; Crosley and Smith, 1982; Jörg et al., 1992, 1990;Lee et al., 1994; Lengel, 1977; Lucht et al., 1986; Smith and Crosley, 1981; Stepowski and Cottereau,1981; Zizak et al., 1981), while there have been less studies investigating the v′ = 1 (Brockhinke et al.,1999; Burris et al., 1988; Kienle et al., 1993; Monkhouse and Selle, 1998; Rahmann et al., 1999) andhigher vibrational levels (Coxon and Foster, 1981; Rahmann et al., 1999). The observations indicatea definite state-specific behaviour, which is fairly well described with a rate constant model based onroom temperature measurements.

Smith and Crosley (1981) used LIF experiments to measure concentrations and population distribu-tion of OH in the burnt gases of methane/air flame at atmospheric pressure. There are some importantfindings about the state-specific behaviour of rotational energy transfer. First, R/Q decreased withincreasing N′. Second, there is a strong propensity for maintaining a spin component (F1 −→F1,F2−→F2). Third, upward transfer from the pumped level produced thermal-like distribution, whiledownward transfer was described by statistical distribution. Although all levels were collisionallypopulated, most of the population was found in rotational levels close to the pumped one. Hence,excitation of a level with low N′ resulted in a distribution predominantly among low levels, whileexcitation to a higher rotational level preferentially populated levels with high N′. A typical narrow-band detector would be centred near the region of highest overall intensity, and would collect all of thefluorescence from low N′ levels, but only a fraction of that from the higher levels. This results in thedetection of a smaller amount of fluorescence for the higher N′, and population for higher N′′ whenthe data are reduced will appear anomalously low. The temperature deduced from a Boltzmann plotis highly sensitive to the populations for high N′′, causing thus systematically low apparent tempera-tures to be obtained from LIF excitation scans. The obvious conclusion is that the rotational energytransfer within the excited state, coupled with finite bandpass detection, can cause massive systematicerrors in rotational temperatures deduced from LIF excitation scans. These effects are minimized oreliminated with use of a wide-bandpass detector, thus the recommendation is to use the most broad-band filter possible. The effects of energy transfer on LIF measurements of flame temperatures canbe avoided or accounted for if the experimenter is aware of their existence.

Crosley and Smith (1982) performed excitation scans in the burnt gases of methane/air flame. Theyused two different detection approaches, a broadband and a narrow (but typical) detector bandpass.The broadband results agreed with the results of Smith and Crosley (1981). A comparison of broad-band and narrowband temperature results show that the differences are minimal for the low N′ num-


bers, but starting with N′ = 8 become noticeable and continue to grow with increasing N′. Whenenergy transfer is accounted for in the narrowband results, the errors are reduced and similar to thebroadband results.

Zizak et al. (1981) studied the rotational redistribution of population of laser-excited hydroxyl mole-cules due to collisions with a thermic bath. They performed measurements in a methane/air flame andused RET in OH LIF to determine temperature. The results showed that steady state can be reachedfor the rotational relaxation of OH radicals in atmospheric pressure flames even during a very shortlaser pulse (typically around 5 ns). The rotational population is redistributed during the first momentsof the laser pulse (Lucht et al., 1980), but equilibrium is reached very fast and these results showsteady state population was established. For levels with quantum number higher than 8 a straightline was observed in the Boltzmann plot of averaged rotational population. This is an indication of aBoltzmann distribution for these levels, thus flame temperature can be determined from the slope ofthis line. The deduced temperature was in very good agreement with other temperature measurementsdone in methane/air flame. Therefore, this study confirmed the possibility of using “thermally-assistedmolecular fluorescence” in determining the local temperature in combustion flows. Also very goodagreement was found between the theoretical prediction and the experimentally observed popula-tions. These findings encourage the use of numerical (computer) work in predicting the rotationalredistribution prior to the experiment and not only in verifying it afterwards. A recommendation wasmade to use a high-power laser to saturate the transition in order to have the most useful experimen-tal approach, together with an optical multichannel analyser to detect the entire spectrum in a singlelaser shot. That approach gives the possibility of obtaining “instantaneous” and spatially resolvedtemperature measurements.

Zizak and Winefordner (1982) performed another study to investigate the application of laser-inducedthermally-assisted atomic fluorescence to determine temperature in gasoline/air flame. LIF processwas presented with a four level system, as an example of a multilevel system. The population of level2, increased by laser pumping, is partially transferred to other levels (3 and 4) by collisions with thehot surrounding gases before being quenched to the ground state. From the ratio of intensities oftwo thermally-assisted fluorescence lines (one coming from level 3 and another from level 4), it waspossible to deduce the flame temperature T . It was confirmed that the relative Boltzmann distribu-tion among the levels is only slightly perturbed by the presence of the laser pulse and that reliabletemperature measurements can be obtained by thermally-assisted fluorescence (THAF) techniques.

Chan and Daily (1980a) developed a form of the rate equations model, based on the experimental re-sults of Lengel (1977), to simulate the dynamic behaviour of OH molecular system. The experimentalspectra was obtained by pumping a series of lower levels (N′ = 1 to 5). These fluorescent spectra werethen compared with calculated spectra. A fit of the numerical model to observed populations is invery good agreement (20% typical) with little sensitivity to the exact values of additional parameters


introduced into the rotational relaxation rate model. The model was used to obtain branching ratioQ22/Q21 for different flame conditions.

2) Vibrational energy transfer (VET)

Vibrational energy transfer has been less studied, and in many cases ignored due to the fact that it isa slower process than RET and quenching. However, vibrational transfer can affect the signal in asimilar way as rotational transfer and cause significant errors in deduced temperature. Excitation tov′ = 1 and observation of fluorescence from molecules collisionally transferred to v′ = 0 is a commonand convenient way to avoid scattered laser light. But, the rate constant of vibrational transfer V andhence the effective quantum yield for this scheme depends on N′. Errors of several hundred degreescan result depending on the range of N′ covered in the experiment. Studies have also been done toinvestigate effects of vibrational transfer in A2 Σ+ state of OH (Burris et al., 1988; Campbell, 1982;Chan et al., 1983; Copeland et al., 1988; Hartlieb et al., 1997; Lengel and Crosley, 1978; Rahmannet al., 1999; Sechler et al., 2009; Smith and Crosley, 1983; Steffens and Crosley, 2000; Williams andCrosley, 1996).

Lengel and Crosley (1978) studied vibrational energy transfer within the A2 Σ+ state of OH, wheremeasurements of the intensities of fluorescence in the (0,0) and (1,1) bands provided the ratio of thepopulations in the v′ = 1 and v′′ = 0. This ratio, as a function of pressure, gives both the 1 - 0 vibrationaltransfer rate and the quenching rate. Several important findings were made from these measurements.First, they found that the transfer rate constants show strong rotational level dependence (decreasingas initial rotational level increases). Second, the final rotational state distributions are near thermalbut hot (population distribution corresponds to higher than real temperature Boltzmann distribution).Third, isoenergetic transfer is small and that the magnitudes for vibrational transfers 1 - 0, 2 - 1, and2 - 0 are all similar and large in magnitude. It was determined that vibrational transfer in OH is inde-pendent of the electron spin component for the same N′, within experimental error. For He collisionsthe R was found to be greater than the vibrational transfer rate constant V . This is according to the ex-pectations concerning energy transfer processes, as the energy level differences for rotational transfer(around 100 cm−1) are much smaller than that for the vibrational transfer (around 3000 cm−1). Theseresults show that the effect of collisions with the surrounding gases cannot be ignored, as they causeboth VET and quenching. The results are supportive of the long-lived collisions in which anisotropicattractive forces are important in the collision dynamics.

Another study of vibrational energy transfer (v′ = 1 −→ v′ = 0) in flames was performed by Smithand Crosley (1983). Their results exhibited a marked decrease in VET rate constant with increasingN′ of v′ = 1. They noticed that a different rotational distribution is established depending on theinitially excited level. Most fluorescence comes from the initially pumped rotational level and onlya small degree of RET within v′ = 1 occurred (mostly to rotational levels near the pumped one) prior


to vibrational energy transfer or quenching. This means that the v′ = 1 −→ v′ = 0 energy transfer thathas occurred can be attributed to the initially pumped rotational level in v′ = 1. Vibrational transferrate constant was observed to be significantly smaller for higher initial N′. The rotational populationdistribution for molecules that experienced vibrational energy transfer showed only mild dependenceon the initially excited level. They hypothesize that these results can be attributed to the role ofanisotropic attractive forces in the energy transfer processes.

Campbell (1984b) developed a sophisticated vibrational-rotational rate equation model for OH forv′ = 1 excitation to study applicability of quantitative LIF in combustion environment. Three collisionpartners were included in the model: N2, H2O and CO2. In each electronic level three vibrationaland forty rotational levels were modelled. The results show qualitatively similar behaviour as forv′ = 0 excitation (Campbell, 1984a). However, the quantitative deviation of the peak number densityfrom the simple two level model is larger than for v′ = 0 excitation, for the same conditions. This wasattributed to the larger VET rate constant out of v′ = 1 than out of v′ = 0 and the smaller saturationparameter for the same conditions when v′ = 1 is excited. The inadequacy of the two level model toaccurately describe collisional dynamics is stressed. Recommendation for future experiments is made:to employ higher laser intensities coupled with v′ = 1 excitation in order to utilize the experimentaltechnique that is least sensitive to collisional rates.

The conclusion of the reviewed publications is that a quantitative treatment must account for quench-ing and in general include a state-to-state description of energy transfer. When the experimental ques-tions are properly designed, useful and important data can be obtained in advance of measurementsusing proper rate equations models.

Polarization

Polarization of the fluorescence is another possible source of error. In LIF measurements with flamethe fluorescence signals are usually collected at 90 with respect to the laser beam. This anisotropycan influence the effective quantum yields, especially if the laser is polarized. In a collision-freeenvironment the emission transition dipole is parallel to the absorption transition dipole. Althoughmolecular rotation reduces the degree of polarization it does not remove it. Collisions usually reducethe level of polarization (the degree of anisotropy) of the fluorescence in two ways (Crosley, 1981):1) elastic dephasing collisions eradicate the directional polarization effects while leaving the moleculein the same level2) collisions causing transfer to other levels can be dephasing at the same time.The observed fluorescence signals can be different from the levels expected assuming isotropic con-ditions, though the errors would most likely be small.


2.1.2 Interferences

Interferences are problems which may serve to mask or distort the signal and they may arise fromthe flow field, such as emission from the flame and diverse forms of scattering. If the integrationtime is decreased by gating the image intensifier, or the spectral bandwidth of the collection opticsnarrowed (thereby rejecting most of the emission interference), emission interference can be reduced.By ensuring that the polarization and the illuminating sheet are perpendicular Rayleigh scatteringmay be reduced. Observing fluorescence at wavelengths other than the pump wavelength (resonantwavelength) reduces Rayleigh scattering, Mie scattering and scattering from surfaces present in thefield of view. Also, surface scattering can be reduced by masking the surface. Another approach isto acquire images of scattering without fluorescence (e.g., by detuning the laser from the optical res-onance being pumped) and subtract them from the images of fluorescence plus scattering (Kychakoffet al., 1984).

Lucht et al. (1984) in their experiments collected the fluorescence at right angles to the laser beam.Only a central vertical slab of the fluorescence probe volume was imaged onto the entrance slit. In thisway, the highest degree of saturation was achieved and the effects of beam steering and defocusingfrom refractive-index fluctuations were minimized.

Morley (1982) observed the fluorescence with monochromator slits wide enough to collect light inthe (1,1) band at 314 nm and (0,0) band at 308 nm. This non-resonant detection evades the noise dueto scattered light, but the downside is that it also reduces the possibility of absorption of the incidentlight before it reaches the scattering point.

In experiments by Palmer and Hanson (1995) transitions in the (1,0) band of OH were excited. Theyused WG305 Schott glass filters to block resonant fluorescence and laser scattering, while the UG5filters were used to block visible radiation. This combination of excitation and detection allowed astrong, non-resonant fluorescence signal to be obtained from the A2 Σ+ - X2 Π (1,1) and (0,0) bandsof OH at 312 and 308 nm, respectively. Additionally, the problem of radiative trapping was mostlyavoided because most of the fluorescence collected terminated in the unpopulated first excited vibra-tional level.

Only when the fluorescence yield goes over a required detection threshold the other criteria, likebeam attenuation or fluorescence trapping, are taken into consideration (Quagliaroli et al., 1993).Frequency doubled dye lasers are able to access many of the OH absorption lines. Because thetypical pulse energy of this laser is not especially high (much lower than the pulse energy of theKrF laser), only high-yield transitions like the 0 - 0, 1 - 0 or the 2 - 0 bands are generally selected forimaging when the OH density is low. The 1 - 0 band is most commonly used to reduce the effectsof beam attenuation by absorption, despite the absorption cross section for the 0 - 0 band being the

Section 2.2 LIF Thermometry 20

largest. Quagliaroli et al. (1993) reported that with the increased density of OH the optical thicknessof the flow is increased. Thus, both the incident laser beam and emitted fluorescence may be stronglyattenuated. By exciting a weaker absorption line the laser beam absorption can be reduced, however,trapping of the emitted fluorescence remains a considerable limitation. In large facilities or at highOH concentration it is expected that the attenuation by absorption and trapping, not being affected bythe transverse spatial distribution of the laser beam energy, becomes even more obvious. This workdetermined theoretically the degree of attenuation of the doubled-dye and the tunable KrF laser beamas a function of OH concentration and optical path length. Even though the OH density distributionis highly nonuniform and unsteady for the most flames, the attenuation is the result of an integrationalong the beam path. Thus, the attenuation can be accurately modelled by multiplying the averagenumber density, nOH , along the incident beam by the distance travelled by that beam through theabsorbing medium. In typical pulsed facilities, where the concentration of OH is large, the doubled-dye laser beam may not be able to penetrate the reacting flow depending on the transition to whichthe laser is tuned to. The solution is to choose appropriate transition to reduce the absorption, or touse the more powerful KrF laser system which has predicted attenuation of less than 20%, even in thepulsed facilities where the concentration of hydroxyl is high. The higher pulse energy of this laserwill partially compensate for the smaller fluorescence yield that accompanies the reduced absorption.Reduced trapping could possibly be obtained by selection of the 2 - 0 band for excitation.

2.2 LIF Thermometry

One general approach to LIF temperature measurements developed by Cattolica (1981) is to excitetwo different lower state levels to the same upper state and observe the relative fluorescence whichis nearly proportional to the relative absorption (and thus the population) in the states pumped. Thetwo lower levels may differ in rotational spacing or belong to different vibrational levels. This wayany excited state collisional effects will cancel out in the ratio of the fluorescence intensities, directlyyielding the ratio of the two level populations. The advantage of this method is that the problemsusually encountered in LIF thermometry (such as quenching, trapping of the fluorescence, sensitivityto detection bandwith) are avoided. Disadvantage of this approach is that lasers at two different wave-lengths are required and the levels must be pumped sequentially which forfeits temporal resolution.In the case that OH number density needs to be deduced from the same measurements the collisioneffects must be taken into account.

In the experiments of Palmer and Hanson (1994) two-line thermometry yielded the rotational temper-ature field by taking the ratio of images generated by exciting two different rovibrational transitionsin two separate laser shots. Lasers pulses used had matching excitation characteristics. Temperaturefields were obtained in two ways: from a single shot image ratio and as a ratio of images averaged forseveral shots. Both methods showed a good match with theory for temperatures above 300 K.


COLLISIONS

VIBRATIONALLEVELS

ROTATIONALLEVELS

0

1

1

0

λ

Figure 2.2: Thermally-assisted laser-induced fluorescence, adapted from Eckbreth (1996)

An alternative approach to two-line pumping requiring only one laser is to use a transition of a specieswith a strong temperature dependence of the fluorescence signal. The main advantage of this methodis that it requires only one laser pulse per measurement, yielding thus temperature based on a single-shot basis (Kychakoff et al., 1984).

It has been demonstrated by several researches (Palma et al., 2003, 1998; Sutton et al., 1993) that laser-induced fluorescence can be used for thermometry in free-piston shock tunnels. However, due to thestrong time-dependent nature of such experimental flows and of turbulent combustion generated inscramjet engines, the methods that are able to yield temperatures in a single facility/laser run, avoidingthus errors based on shot-to-shot flow fluctuations, are especially appealing thermometry techniques.Thermally-assisted laser-fluorescence thermometry methods are able to yield reliable results fromsuch single-shot measurements, they are relatively experimentally simple and potentially insensitiveto absorption effects. They are, however, possibly sensitive to systematic error due to their sensitivityto energy transfer rates.

2.2.1 Thermally-assisted laser-fluorescence thermometry

A method of obtaining temperatures using LIF on OH was developed by Chan and Daily (1980b).Individual rotational levels in v′ = 0 were excited and rotationally resolved fluorescence spectrum fromthat vibrational level was observed. The spectra were fit to the model (Chan and Daily, 1980a) and


the temperature was considered as a parameter determined by fitting procedure. They achieved goodagreement with thermocouple measurements in the methane-air flame over the range 1880 to 2010 K.The sensitivity of the deduced temperature to the results comes mainly through populations of levelswith high N′ because these levels are populated through upward transfer with rate constants linkedto those of the downward energy transfer by detailed balancing. The fluorescence spectrum in theirstudy was obtained by scanning the monochromator and averaging over many laser pulses, however,single-shot results could be achieved using an optical detector able to record the entire fluorescentspectrum at once.

As mentioned earlier in this chapter, Zizak et al. (1981); Zizak and Winefordner (1982) have donemeasurements in different flames to investigate rotational energy transfer as a flame thermometer.Their results have shown good agreement with different measurement techniques and theory, thushave proven that the thermally-assisted fluorescence technique has the ability to give reliable resultsin combustion diagnostics.

The method of vibrational energy transfer as flame thermometry technique was firstly demonstratedby Crosley and Smith (1980). In their measurements they excited a line in the OH (0,0) transitionband, and using the ratio of intensities of the (0,0) and (1,0) band they were able to determine vibra-tional temperature with an error of ± 60 K. These results are within a reasonable agreement with theresults of an excitation scan. This method is also able to yield temperature in a single-shot manner ifthe detection system is able to record at once fluorescence from two different vibrational bands.

To obtain temperature, they applied steady-state approximation for population balance to the v′, whichyields

Vie Ni = (Vei +A+Q)Ne (2.1)

where Vie is the upward vibrational rate constant (i = initial, e = excited) and Vei is the downward rateconstant from the excited to initial level, A is the radiative emission rate constant for spontaneousemission from the excited state, and Q is the quenching rate constant to all other levels. Ne and Ni

are the populations of the excited and initial level, respectively. The upward vibrational transfer rateconstant, according to equation 2.2, is related to the downward rate constant by detailed balancing.

Vie =Vei exp(−∆Eei/kBT ) (2.2)

Since A «V and Q, neglecting A and rearranging yields

Ne

Ni=

exp(−∆Eei/kBT )1+Q/Vei

(2.3)


and vibrational temperature is obtained by

T =(−∆Eei/kB)

ln[(1+Q/Vei)NeNi]

(2.4)

Thus, temperature can be determined through the knowledge of the relative populations of the excitedand ground vibrational levels, and the ratio of quenching to vibrational transfer, Q /V . Relative popu-lations are obtained by measurement of the band intensities and the use of the Einstein A coefficient.

Joklik (1992) showed the usefulness of VET THAF with measurements in the post flame regionof several laminar premixed flames. A simple two-level model that takes into account electronicquenching and VET was used. Variation of Q/V ratio of the v′ = 1 state for a wide range of equivalenceratios and fuels was given. Temperatures were deducted with an error of ± 50 K compared to thesodium-line reversal measurements and checked with OH ground state rotational temperature (byabsorption), for the averaged results. The single-shot results show a somewhat lower accuracy.

The experimental results of Neuber et al. (1996) is another demonstration that thermally-assisted fluo-rescence of laser-excited OH radical is a technique that is easy to apply for measurements of tempera-ture and OH concentration in turbulent atmospheric diffusion flames. They performed turbulent flametemperature and OH concentration measurement in atmospheric pressure non-premixed flame wherev′ = 0→ v′′ = 0 transition was excited. Through evaluation of the emission from the v′ = 1→ v′′ = 0and v′ = 2 → v′′ = 1 bands with a full spectral fit they were able to evaluate the temperature and theOH molecule density (concentration). No correction of the signal was needed due to modelling of thecomplete LIF process, including all intermediate sub-processes such as photon absorption, molecularelectronic quenching, VET, RET. The major problem with that approach is the understanding of thecollision dynamics of the excited molecules with their neighbouring molecules. The evaluation the-ory is based on a simple model that takes into account only quenching and VET (Figure 2.3). Thepresented data was spectrally and temporally averaged.

All experimental spectra were fitted by theoretical spectra by minimizing the least-squares sum, andthe main fit parameters are the OH concentration cOH , the temperature T , and the spectral shift. LIFtemperatures error is ±100 K for those flame locations that give more than 75% of valid spectra (Fig-ure 2.4a). For the rest there is not enough OH in the measurement volume and the statistic is biasedtoo much. However, there was no biasing of the OH concentration because in the averaging proceduremole fractions lower than 10 ppm (which is the detection limit) can be set to zero with a small erroronly. The mean OH concentration profiles diverge in both position and spatial width. The reason isthat the combustion model assumption of chemical equilibrium holds only for the major species butnot for the radicals like OH. Both experimental and theoretical concentrations are normalized at themaximum value, thus giving no information on the absolute value of OH concentration.


N0

V10

A1+Q1

N1

N2

pump loss

V01

V02

V20

V12 V21

A2+Q2

OH A2Σ+ excited state

Figure 2.3: Energy-level diagram of the first electronic state of OH molecule, A2 Σ+, reproduced from Neuberet al. (1996). First three vibrational levels (v = 0, 1, 2) are shown. This model takes into account only thevibrational energy transfer and quenching.

Figure 2.4: Results from Neuber et al. (1996). a, open circles, variation of experimental mean temperaturewith the flame radius at the flame level x/D of flame with mass fraction H2 = 20%; solid curve, calculated meantemperature; filled circles, experimental standard deviation of the temperature caused by turbulent fluctuations;dashed curve, calculated standard deviation. b, fraction of spectra with high enough intensity for a successfulevaluation 1in percentage2. c, open circles, experimental mean OH concentration in molecules per volume, nor-malized to 100; solid curve, calculated mean OH concentration, normalized to 100; filled circles, experimentalstandard deviation of the OH concentration.


The harpooned model (Paul, 1994) for temperature-dependent quenching gives a maximum variationof 33% for the cross section with H2O as collision partner in T = 1000 K to 2000 K temperaturerange. Conclusion is that the main uncertainty in the temperature determination with full spectral fitoriginates from the assumption of thermal equilibrium of the collision populated levels v′ = 1, v′ = 2(the error is estimated to be 3% with N2 as the collider molecule). They pointed out that this goodagreement in temperature and simulation occurs only when there is sufficient OH concentration inthe measurement volume. If electronic quenching is the dominant collision process compared withVET, the ratios of the vibrational rate constants V20 / V10 and the electronic quenching rate constantsQ2 / Q1 are nearly equal. The unknown energy transfer rate constants (Q, R, V ) influence the overallmeasurement error.

Thermally-assisted fluorescence of laser-excited OH A2 Σ+ based on energy transfer have been provena promising method for temperature measurements. This method is relatively simple and potentiallyinsensitive for absorption effects, if the excitation wavelength is properly chosen. In addition, it shouldbe relatively simple to extend it to 2D temperature imaging. Depending on the spectral resolution andbandwidth possible to obtain in measurements, either THAF based on RET or VET can be done.With a rotationally resolved fluorescence spectrum rotational temperature can be deduced, possiblyfrom the branching ratios. If the obtained spectrum does not show adequate rotational resolution, butthere are at least two different vibrational bands recorded, vibrational temperature can be derived.Therefore, in the present study, an adapted version of thermally-assisted LIF thermometry will beimplemented and modelling of the OH LIF process will be done. This approach will enable thiswork to obtain the first ever single-shot temperature measurements in scramjet experiments. In theturbulent combustion process of a scramjet engine it is necessary to obtain all the information in onesingle-shot, which makes this approach to thermometry ideal for use in scramjet flows. Chapter 4gives more details.

Chapter 3

Spectral Modelling

3.1 OH modelling

LIFBASE (Luque and Crosley, 1999), SPARTAN (Lino da Silva, 2007) and Photaura (Potter, 2013)are numerical programs able to simulate gas radiation and produce synthetic spectra. These spectracan be used in the design phase of the experiments and in the analysis phase for validation of theexperimental results. All three programs are free and available. However, in order to validate ex-perimental data in this work a simulation program providing synthetic spectra of the OH radical isneeded. Originally, only LIFBASE contained OH molecule in its radiation database. However, thelack of LIFBASE source code and consequent uncertainty of the transition modelling process createda need to include OH in the programs for which the source codes are available. The SPARTAN code(Simulation of Plasma Radiation in ThermodynAmic Nonequilibrium) is a numerical code for spectralsimulation of absorption or emission process of a gas that can be either in thermodynamic equilibriumor in nonequilibrium state. The source code was provided by the author Mario Lino Da Silva, andthe presented results were obtained with the latest version SPARTAN 2.6.alpha (unofficial version).A limitation of SPARTAN was turned into one of the objectives of this work - a creation of an OHdatabase that was added to the existing species database of SPARTAN. LIFBASE was subsequentlyused for validation of the spectra obtained by SPARTAN during the process of implementation ofhydroxyl radical into the SPARTAN. The approach that was used in the process of implementationand comparison is based on input files that contain both spectroscopic constants based on electroniclevels, as well as vibrationally-specific constants.

Another code that had to be modified to include the OH is Photaura. The Photaura code is a hightemperature gas radiation module for compressible flow CFD, a part of the University of Queensland’sCompressible Flow CFD group’s present code collection. The source code was developed by DanielPotter and obtained from the group’s main repository. The availability of this source code is the reasonwhy Photaura was chosen, alongside with SPARTAN. The drawback of Photaura is that originally itdid not contain OH which then had to be added to the existing species database. LIFBASE, and

Chapter 3 Spectral Modelling 27

SPARTAN, whose database was also modified previously to include OH, were subsequently usedfor validation of the spectra obtained by Photaura during the process of implementation of hydroxylradical into Photaura. Photaura code is currently based on the spectroscopic constants per electroniclevel only, therefore the input files contain spectroscopic constants based on the electronic levels only.

The availability of these source codes that can be tailored to meet our needs is the reason why SPAR-TAN and Photaura were chosen. In order to have a proper comparison of the spectra obtained withthree different codes it is crucial to have inputs and conditions the same. The lack of LIFBASE sourcecode makes this a difficult task. The LIFBASE input files we do have access to have been used aswell as input in SPARTAN and Photaura databases. The conditions of the simulations were kept thesame as much as three codes allow it in the present state.

The numerical codes SPARTAN and Photaura were modified in order to include the hydroxyl radical.Probably the most comprehensive study of the A2 Σ+←→X2 Π system of OH was done by Diekeand Crosswhite (1962). In this thesis, however, in order to keep the input data between the spectralsimulation codes as consistent as possible, LIFBASE input files data were used as input in SPARTANand Photaura databases when possible. In the cases when required information was not available fromthe LIFBASE input files, other relevant studies were used as sources. The results of the SPARTANand Photaura spectral simulations were then compared with the results of the LIFBASE simulationthat already contains OH in its database. In addition, a comparison was made with the experimentalresults of the inlet-injection supersonic combustion study (Brieschenk et al., 2013; Lorrain, 2014) tosee how these synthetic spectra correlate to the experimental one.

3.1.1 SPARTAN

This section presents details of the input files used by SPARTAN. The nomenclature here was keptsame as in the original files as to make it easier for the reader who wishes to alter the conditions ofsimulation (such as temperature, species number density, etc.). Also, if one decides to add anotherspecies to this simulation code, the information presented here should help make that process easier.

The OH-G.txt and OH-LEV.txt files are OH species input files. There are three additional SPAR-TAN text files that need to be modified in order to implement new species into the code. These areDatabase.txt, Inputs.txt and Guinterface.txt. For every species included in the radiation database ofSPARTAN the same kind of information is needed in these files, but the values naturally change foreach species. Database.txt file contains the information about the transition that is simulated. In-puts.txt incorporates the information about the particular species whose transition is simulated andthe conditions of simulation. Guinterface.txt gives details on the section of the GUI interface ofSPARTAN code for that particular species. In the Database.txt, Inputs.txt and Guinterface.txt files theOH species-specific input data looks as in Table 3.1, Table 3.2 and Table 3.3, respectively.

Section 3.1 OH modelling 28

Table 3.1: Database.txt file particular species line.

Notation in the file Meaning of the entry

OH_AX Transition nameOH Chemical species symbol0.01700394 Molar mass [kg mol−1]OH-G.txt Radiative transition fileOH-LEV.txt Molecular energies file2 Identifier of the upper electronic level1 Identifier of the lower electronic levelBoundDI Type of the transition2S—2P Detailed transition identifierBoltzmann Population of the levels

Table 3.2: Inputs.txt file particular species line.


3000 Rotational temperature [K]3000 Vibrational temperature [K]3000 Translational temperature [K]1e+00 Species number density [cm−1]OH Chemical species symbol0.01700394 Molar mass [kg mol−1]0.50011 Radius [Angstrom]

Table 3.3: Guinterface.txt file particular species line.


OH AX Doublet Transition name1.0 RGB color specification0.5 RGB color specification0.5 RGB color specification370 X position115 Y position130 Length of the name15 Width of the name


Input file: OH-G.txt: Spectroscopic constants per both electronic level and vibrational level

The OH-G.txt file contains most of the information needed for a transition. First input data are Klein-Dunham matrices consisting of spectroscopic constants for both excited and ground electronic level.Dimensions of the matrices are 10 x 7 - enough to take into account all of the polynomial expressionsproposed in literature when calculating line positions (Lino da Silva, 2004). The first matrix in thisfile is always the one for the excited state and the second one is for the ground level. The Klein-Dunham matrix is followed by specified γ values for the A2 Σ+ excited electronic level, intended fordescription of fine structure (only if spin-doubling is taken into account). In all the input files theseγ values acquired from Huber and Herzberg (1979) were kept fixed. For the X2 Π ground level thevalue of spin-coupling constant Av is stated. This constant is in the form of polynomial expression asin equation 3.1.

Av = X1 +X2(v+0.5)+X3(v+0.5)2 +X4(v+0.5)3 (3.1)

The values for X1, X2, X3 and X4 in Equation 3.1 were given by Coxon (1980) and they were keptfixed in all the OH-G.txt input files.

Additionally, the values for Nuclear Spin Statistical Weight, explicit values, perturbations, number ofrotational and number of vibrational levels must be given. JEmax and JGmax are not defined in thecode, and they are put in each of these text files as a random value (999) and there are as many of thesesets of values as there are vibrational levels (the comment by author says these will be implementedin newer version of SPARTAN).

The spectroscopic constants per vibrational level were taken from Luque and Crosley (1999).1 Ex-plicit values have to be set to 1 in this case. Data is given firstly for the excited and then for the groundlevel. Values for the number of vibrational levels and exact vibrational levels taken into account needto be specified, as well as values for the number of variables included and explicit variables in thecode.

The next variable to be altered is the Franck-Condon factors matrix (size is equal to the numberof vibrational levels, i.e. for v = 8 the Franck-Condon matrix is 8 x 8) and the last data necessary toinclude in this file is the matrix of Einstein A coefficients with dimensions equal to the Franck-Condonfactors matrix.

Spectroscopic constants for each vibrational level included in the simulation are given in Table 3.4.

1However, their actual origin has not been revealed entirely. LIFBASE doesn’t reference it, although through investi-gation by comparison with published spectroscopic data for OH the origin of these values was found for the most of theconstants. All the LIFBASE input constants and references can be found in the Appendix C.


Table 3.4: Vibrationally-specific variables.

Variable Notation

1 ν02 Bv3 -Dv4 Hv5 Lv6 Mv7 Av8 γ

9 γJ10 γJJ

In the current version of the input file not all rotational constants were included in calculation, theequations for doublets stops at Hv in SPARTAN. Higher order rotational constants (Lv and Mv) arecurrently not computed in the SPARTAN code. Also, γJ and γJJ are set to zero in the code, whichshould be changed in the future versions of the program, when these variables will be read from theinput files instead. Another difference in the input values between LIFBASE and SPARTAN is thatΛ-doubling constants p and q have not been included in SPARTAN input files. The SPARTAN codein its current version does not take these into account. The next step would be to implement the restof rotational constants, as well as γJ , γJJ and Λ-doubling constants p and q in SPARTAN and see theirinfluence on the results.

Input file: OH-LEV.txt:Calculation of partition functions for diatomic species

This input file is needed when implementing diatomic species in SPARTAN to compute partitionfunctions. The first entry gives the number of electronic levels in the diatomic molecule considered,two in this case. The second line specifies nuclear spin degeneracy, which is 1 for heteronuclearmolecules like OH.

Subsequent data provides information for the calculation of partition functions for each of the elec-tronic levels involved in the transition. Table 3.5 is an example of the OH-LEV.txt file with the valuesfor spectroscopic constants given by Luque and Crosley (1998). Dissociation energy values for eachof the electronic levels were taken from Ruscic et al. (2002).

3.1.2 Photaura

Details of conditions and input files are given Table 3.9. The radiator_ library.py, OH.py and OH-radiators.py files are OH species input files, and certain files’ inputs are reported as in Table 3.6,


Table 3.5: OH-LEV.txt file electronic level data.

Notation in the file Meaning of the entry 1st entry 2nd entry

State Electronic level name X AMode Calculation mode for 0 0

the vibrationalpartition functions

Te Electronic energy [cm−1] 32684we Vibrational frequency [cm−1] 3737.7941 3178.3554Be Rotational constant [cm−1] 18.89638 17.38922α Rot.-vib. interaction constant [cm−1] 0.725042 0.858139D0 Electronic level 35593 18956

dissociation energy [cm−1]ge Electronic level degeneracy 2 2

Table 3.7 and Table 3.8, respectively.

Input file:radiator-library.py

Photaura code uses Python based input files. In the case of OH these are radiator_ library.py, OH-radiators.py and OH.py input files. The radiator_ library.py file contains most of the informationneeded for a transition. First input data gives the information on what type of radiator is the chosenspecies. This is followed by information about the particular species, such as name, molecular weightor dissociation energy. Spectroscopic constants per electronic level only are in the form of a matrix,containing constants for both (or more) electronic levels involved in the transition. The remainderof data gives information on the transition, i.e., the electronic levels involved in the transition, typeof transition probability constants used and the matrix dimensions. In the present study Einsteincoefficients are used, obtained from LIFBASE database. The last information in this input file isabout the photoionization (not applicable here) and quasy-steady state model.

Input file:OH-radiators.py

The input file including information for definition of a radiation model. It includes values for thewavelength range, species included in simulation and information about which particular species areradiating.

Input file:OH.py

This input file contains data about the species observed and simulation inputs, such as pressure, tem-perature and instrumental broadening.


Table 3.6: radiator_ library.py file particular species line.

Notation in the file Value of the entry Meaning of the entry

OH DiatomicRadiator Specifying radiator typeOH Chemical species symbolmol_weight 0.01700394 Molar mass [kg mol−1]h f 2.292e+6 Specific formation enthalpyZ 0 Charge numberηI 104989.14 Ionization energy [cm−1]ηD 38450 Dissociation energy [cm−1]

corresponding to 460 [kJ mol−1]AX .iel 0 Ground electronic level identifierAX .ieu 1 Excited electronic level identifierAX .band_method linebyline Excited electronic level identifierbands.format Einstein coefficient Excited electronic level identifier

Table 3.7: OH-radiators.py file particular species line.


gdata.spectral_model photaura Specifying radiation model usedgdata.lambda_min 300.0 Minimum wavelength in the range usedgdata.lambda_max 330.0 Maximum wavelength in the range usedgdata.spectral_points 2.292e+6 Number of point in spectral calculationspecies OH Symbol of the species consideredradiators OH Symbol of the radiators considered

Table 3.8: OH.py file particular species line.


species OH Symbol of the species consideredmass_fractions 1.0 Mass fractions of the particular speciesmole_fractions 1.0 Mole fractions of the particular speciesgas_pressure 101325 Pressure of the gas [Pa]gas_temperature 3000 Temperature of the gas [K]path_length 0.1 Width of gas [m] that is integrated across

when computing the intensity spectraapparatus_fn Voigt Resultant spectral distribution functionGaussian_HWHM 1.25 Instrumental broadening [Å]Lorentzian_HWHM 0 Pressure broadening [Å]sampling_rate 1 Number of samples (points) per unit of timeproblem pT Pressure and temperature dependent problem


3.1.3 Comparison of SPARTAN, LIFBASE and Photaura synthetic spectra

The electronically excited OH particles redistribute their energy through radiative decay and collisionswith the surrounding particles. Emission of radiation for OH occurs at wavelengths around 281 nm,306 nm and 343 nm. Equation 3.2 gives the spectral irradiance (Potter, 2011):

Iν =jκ(1− e(−κdx)) (3.2)

where Iν stands for spectral irradiance, j is the emission coefficient, κ is the absorption coefficient,and dx is the flow path.

In the limit of very small dx or very small κ (“optically thin”), the expression for the spectral irradi-ance, equation (3.2), reduces to:

Iν ≈ j ·dx (3.3)

The source is considered to be “optically thin” if all emitted radiation reaches the spectrometer withoutbeing re-absorbed (Thorne, 1974). LIFBASE and SPARTAN assume the optically thin case, whilePhotaura by default assumes optically thick flow with the intensity given by Equation 3.2.

While performing the simulations, the input parameters were kept the same in all numerical codeswhen possible. Table 3.9 gives information on these input parameters. Thermal Doppler broadeningis considered in the numerical simulations of the spectra presented in this paper, while collisionalbroadening is neglected, except in the SPARTAN code, which considers collisional broadening bydefault. This does not present a noticeable difference in the results and can be neglected.

Table 3.9: Input parameters in spectral simulations.

Parameter LIFBASE SPARTAN Photaura

Apparatus function [nm] 0.25 0.25 0.25Temperature [K] 3000 3000 3000Line broadening Doppler Doppler Doppler

CollisionalResonanceVan der Waals

Wavelength range [Å, air] 3000-3300 3000-3300 3000-3300

Figure 3.1 shows some difference detected between the synthetic spectra. Slight discrepancies are ob-served in this comparison and these could be because of constants or modelling broadening processesapplied. Not all the constants used in these programs are the same, and small differences exist in thechoice of spectroscopic constants used. This is due to the fact that it was not possible to implement

Section 3.2 T4 shock tunnel experiments of Lorrain 34

all of the LIFBASE input data in SPARTAN and Photaura. For example, in addition to the constantsper electronic level, SPARTAN also uses the vibrationally-specific spectroscopic data, while Photaurainput files use constants per electronic level only.

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Figure 3.1: Comparison of the OH spectra obtained using different programs.

3.2 T4 shock tunnel experiments of Lorrain

The spectrally resolved measurements of the OH* emission spectra have been conducted in the T4free-piston shock tunnel at The University of Queensland using a Mach 9 enthalpy-equivalent flightcondition, and described in detail in Lorrain (2014) and Brieschenk et al. (2013). The flowpath of thescramjet model is two-dimensional and rectangular in cross-section with a constant area combustor.Fuel was injected through four 2-mm-diameter port hole injectors, angled 45 degrees to the wall. Thetest conditions are found in the Table 3.10.

Table 3.10: Flow conditions in experiments of Lorrain et al. (2014).

Total flow Freestream Enthalpy-equivalent Fuel injectionproperties properties flight condition properties

H0 = 3.74 MJ/kg u∞ = 2685 m/s M f light = 9 pplenum = 1310 kPaT0 = 3228 K T∞ = 314 K q f light = 71 kPa m f uel = 16.8 g/sp0 = 44.2 MPa p∞ = 3650 Pa h f light = 29.6 km φ = 0.8

M∞ = 7.54pPitot = 2.66 kPa

Experiments were performed as two-dimensional visualisation, and spectrally resolved. For thetwo-dimensional visualisations, the ultraviolet signal was captured using an intensified CCD cam-


era (Princeton Instruments PI-MAX3) together with a 50 mm focal-length quartz lens (Goyo OpticalGMUV55035C). The ultraviolet signal was filtered using a 10-nm-FWHM bandpass filter centred at310 nm (Asahi Spectra ZBPA310) to capture fluorescence emitted around that wavelength, and block-ing everything else. Exposure times greater than 10 - 100 µs were typically required. An exposuretime of 1.5 ms was chosen for the chemiluminescence recordings presented in this work. Spectrallyresolved measurements were obtained by adding a 270-mm-focal-length f / 4 spectrometer (SPEX270M) in between the ICCD camera and the UV lens. A 2400 l/mm grating was used in combinationwith an entrance slit width of 50 µm. The entrance slit of the spectrometer was located approximately0.6 m from the longitudinal axis of the scramjet model. A UG5 filter was mounted on the entranceslit to increase the rejection ratio of the spectrometer that would otherwise appear in the chemilumi-nescence recordings. To increase signal-to-noise ratios, the f-number of the lens was matched to thef-number of the spectrometer. The optical path between the scramjet model and the shock tunnel wasenclosed by shrouds to reject luminescence that is generated elsewhere in the test section/dump tankof the facility. Thermal choking for this scramjet geometry occurred for equivalence ratios close toφ = 1, thus the equivalence ratio was kept at φ = 0.8 to ensure the scramjet model did not unstart duringthe test time. Unstarting could have caused damage to the ICCD camera due to the overexposure.

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∆L=1.0m∆L=0.5m

∆L=0.2m∆L=0.1m

∆L=10-2m∆L=10-3m

∆L=10-4m∆L=10-5m

∆L=10-6m∆L=10-7m

Figure 3.2: Phtoaura: Intensity range from optically thin (∆L=1e−7 m), lowest intensity curve, to opticallythick flow (∆L=1 m), highest intensity curve. Simulations done with T =3000 K.

Spectrally resolved measurements were taken at three downstream locations. The slit locations are at60 mm, 90 mm and 335 mm, measured from the start of the combustor. Figure 3.3 presents a compar-ison of these experiments with the results of spectral simulations. As each of the three slit locationscorresponds to different flow conditions, i.e. different stages of combustion process, numerical simu-lations were done with different conditions, and compared with each slit location separately. Each slitlocation result was compared with all three synthetic spectra corresponding to the optically thin flow.

Section 3.2 T4 shock tunnel experiments of Lorrain 36

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Figure 3.3: Comparison of synthetic spectra with experimental results of Brieschenk et al. (2013); Lorrain(2014).


The observed difference between experimental and synthetic spectra, increasing with the increase inthe wavelength, is an indication that the experiments show a departure from the optically thin case,and that in reality even the first slit location, at the combustor entrance, doesn’t correspond to theideal case of optically thin flow. It has been said previously that Photaura by default gives numericalspectra for optically thick flow, but it can also simulate optically thin flow. Figure 3.2 shows the tran-sition, in the form of spectral irradiance, from optically thin to optically thick flow. The experimentalresults were therefore further compared with the optically thick flow simulations, calculating opticalthickness for each case separately. A good match with the result of Photaura’s optically thick case wasobtained, with optical thickness varying between slit locations and being the greatest for the third slitlocation at the end of the combustor. Figure 3.3 shows the discrepancy that exists between opticallythin and optically thick conditions for each of the slit locations and how this discrepancy changes withthe change of the location along the combustor length.

3.3 Summary

The results presented in this review show that OH spectra produced with different programs showvery good agreement. There are several reasons for the slight discrepancies between three programs.Firstly, the source codes have different radiation modelling. Calculation of parameters that influencethe spectra considerably can be performed in a different way resulting in discrepancies observedbetween three spectra. Secondly, even though most of the spectroscopic constants are the same inboth SPARTAN and Photaura input files, each of these codes still uses some specialised inputs aswell. This can produce some discrepancies in simulation results.

In comparison with the spectrally resolved OH* emission spectra, synthetic results demonstrated avery good agreement. The reason for discrepancies could be the spectral signature of other speciesradiating in the same wavelength (such as CH) and influencing the results, improper calibration of theoptical setup used, or incorrect assumption of thermal equilibrium. Also, the origin of the discrep-ancies might be the imperfection of the numerical programs resulting in the small differences whenresults are compared with the experimental results. The comparison of the synthetic spectra with theexperimental data indicates that results of the LIFBASE, SPARTAN and Photaura spectral simulationcannot be considered a fully valid representation of the physical phenomena occurring in the scramjetcombustion.

Chapter 4

Experimental Approach

For the application of the proposed thermometry method to be realised in practical scramjet con-figurations, experiments must be conducted using a realistic scramjet combustor. In this project, athermal compression scramjet model was used; in which, the proposed thermometry method was ap-plied to measure temperatures in the combustor region. These experiments were conducted in the T4free piston shock tunnel facility at The University of Queensland (Stalker et al., 2005), with the newexperimental optical diagnostic arrangement to implement the LIF, PLIF and emission spectroscopymethods. This chapter includes a description of the new LIF system set-up in the T4 facility, followedby a description of the scramjet model used for the supersonic combustion experiments. The testconditions, along with the uncertainties and repeatability analysis, are then presented. The chapterends with a description on how the pressure data in the scramjet model is processed for this study.

4.1 LIF system set-up in the T4 shock tunnel

The T4 shock tunnel facility at The University of Queensland, as shown in Figure 4.1, is a free pistondriven reflected shock tunnel impulse facility, which is capable of producing high speed flows withtotal enthalpies of up to 15 MJ/kg. This ability to produce high total enthalpy flows enables thepossibility for one to conduct true supersonic combustion experiments in this facility - it is for thisreason that the T4 shock tunnel was chosen for the experiments in this study. With this ability comesa major disadvantage: the flow durations available are limited to just several (1-5) milliseconds ofsteady test time. This limitation, however, does not affect the findings of this study, as will be laterdiscussed in this chapter. Detailed descriptions of the operation of this test facility can be found inreports by Stalker and Morgan (1988) and Stalker et al. (2005).

For the proposed LIF thermometry method to be implemented in the T4 shock tunnel, a new opticalsystem was built around the test section of the facility. Figure 4.2 shows this optical set-up.

Several modifications were performed in the T4 test facility in order to make LIF experiments possi-ble. A new optical table was acquired, laser curtains were installed, and the test section was modified

Chapter 4 Experimental Approach 39

Figure 4.1: Layout of the T4 free-piston shock tunnel (Doherty, 2013).

dump tank

Mach 8B nozzle

scramjet model

spectrometer

ICCD camera

dichroic mirrors

laser beam

test section

Figure 4.2: Optical set-up, LIF configuration.

Section 4.1 LIF system set-up in the T4 shock tunnel 40

to allow optical access to the scramjet model for LIF purposes. A detailed description of these modi-fications is given in the PhD thesis by Vanyai (2017).

4.1.1 Experimental Arrangement of the LIF system

The primary requirements for laser-induced measurements are a tunable laser light source, an imageintensified camera, a fluorescence detector, and a data acquisition, processing and display system.

A laser is by far the best way to provide a light source of high spectral irradiance and laser excitationis also spatially, temporally and spectrally resolved. There are a few laser systems available for theexcitation of transitions in the A2 Σ+←X2 Π band of OH (Quagliaroli et al., 1993):

• Dye laser, following frequency doubling or mixing, can be tuned to a resonance with any tran-sition in the 0, 1, 2, 3← 0 bands

• XeCl excimer laser, resonant only with transitions in the 0← 0 band

• KrF excimer laser, resonant only with transitions in the 3← 0 band

The dye laser offers the most versatility in the selection of transitions, and is an obvious choice forlaser system. Because visible dyes are usually more efficient and longer lived than UV dyes, thecommon approach is to frequency double the output of a visible dye laser rather than to work with anUV dye. Also, UV dye lasers need to be pumped at a lower wavelength than the visible dye lasers,which might present a problem considering the pumping source. For pulsed dye lasers the mostcommon pumps are flashlamps, Nd:YAG lasers, nitrogen lasers, and excimer lasers. Pulsed lasers aregenerally more useful for species and temperature visualization because the short duration (and highspectral irradiance) of the pulse enables one to freeze the motion in the flow field and reject certaintypes of interference. Unfortunately, the pulse rate of these lasers is often low (on the order of tensof Hz) which limits the achievable recording rate. The fluorescence intensity is usually too low to bemeasured directly with conventional imaging detectors and an image intensifier must be used. Forpulsed laser sources the duration of the pulse, ti, can be very short, but the repetition rate of the lasermay be as low as a few Hz. The net result: the motion in the object plane is nearly frozen, but it isdifficult to correlate successive frames. Kychakoff et al. (1984) stated that the optimum light source(for species and temperature measurements) is a pulsed laser of short pulse duration and a repetitionrate which is comparable to the maximum array readout rate.

The laser system also influences the choice of the transitions which one is able to excite. Due tothe high population density in the ground vibrational state the majority of LIF methods involve theexcitation of molecules from the v′′ = 0 level. However, the selection of the upper vibrational levelv′ depends on the experimental requirements and the available laser system. The largest Einstein B


coefficient (coefficient rate for absorption from the ground level) is for a v′ = 0← v′′ = 0 ro-vibronicabsorption. For higher v′ the Einstein B coefficient decreases rapidly with the increase of v′, thuslimiting LIF applications to excitations of v′ ≤ 3. Following 0 - 0 excitation, most of the fluorescenceis in the 0→ 0 or 0→ 1 band area, producing a strong signal. However, observing the fluorescence inthe same wavelength range as the incident laser may cause interferences from the laser light. Thus,fluorescence is typically separated from the laser light by choosing different excitation and fluores-cence wavelengths. Additionally, because of the strong absorption in the 0 - 0 band, the laser beam isattenuated and the emitted fluorescence is reabsorbed (trapped) even in small-scale facilities. Thus,the use of this excitation band is not recommended. The most common alternative approach is toexcite a transition in the OH (1← 0) band, with a relatively strong subsequent fluorescence.

Based on the presented characteristics of available laser systems and excitation schemes, the excita-tion of A2 Σ+←X2 Π (1 - 0) band by the doubled-dye laser was chosen for the present study. There-fore, a dye laser was purchased which to be used together with Nd:YAG laser that was already a partof the facility capabilities.

To capture the ultraviolet signal an intensified CCD (Princeton Instruments PI-MAX3 GENII) wasused in all experiments. The CCD chip used in the camera is 13.1 mm× 13.1 mm in size and offers amaximum resolution of 1024 px× 1024 px. The camera was mounted on a frame, which was attachedto the test section window flange and allowed for vertical and horizontal adjustments of the cameraposition. The scramjet model and test section were fitted with fused silica windows on the side ofthe ICCD camera. The object distance between the longitudinal axis of the combustor and the lens of0.45 m was adjusted so that, for the two-dimensional measurements, the respective imaged combustorsection was projected onto the entire imaging area (both width and height) of the sensor array. Thecombustor section captured was approximately 355 - 505 mm from the start of combustor intake, orapproximately 175 - 325 mm from the combustor entrance.

LIF optical arrangement

Laser-induced fluorescence measurements were spectrally resolved by placing a 270-mm-focal-lengthf / 4 spectrometer (SPEX 270M) in between the ICCD camera and the UV lens. A 50 mm focal-length quartz lens with aperture of f / 3.5 (Goyo Optical GMUV55035C) was used for all LIF scram-jet recordings, while a 2400 l/mm grating was used in combination with an entrance slit width of100 µm. The entrance slit of the spectrometer is located at about 0.307 m from the entrance of thescramjet combustor. The ultraviolet signal was filtered using a WG305 filter (Edmunds optics) anda UG5 filter (Thorlabs), that were mounted on the entrance slit to increase the rejection ratio of thespectrometer and suppress laser scattering and other flow artefacts that would otherwise appear in theLIF recordings. An exposure time of 300 ns was chosen for all the LIF recordings presented in thiswork.

Section 4.2 LIF system set-up in the T4 shock tunnel 42

Emission spectroscopy optical arrangement

One-dimensional spectrally resolved emission measurements were obtained with the same optical ar-rangement (spectrometer, lens, filters) as LIF experiments, but without the laser. The emission signalof the hydroxyl radical is several orders of magnitude weaker than the laser-induced OH fluorescencesignal. Additionally, long camera exposure times, greater than 10-100 µs, are typically required toaverage out turbulent fluctuations in the recorded images, and thus obtain a steady state intensity dis-tribution of the emission signal. An exposure time of 1.5 ms, centred around the test time intervalused for the pressure integration, was chosen for one-dimensional emission recordings.

PLIF optical arrangement

For two-dimensional (PLIF) experiments the laser beam was passed through a cylindrical lens todiverge and widen the beam prior to passing through the converging, plano-convex lens. This way alaser sheet with a constant width is created. Before entering the test section and scramjet model, thelaser sheet passes through a beam splitter. This optical component is used to separate the sheet in two,letting through the majority of radiation while directing a small amount to a dye cell. The dye cell isutilized for calibration and monitoring of the laser sheet intensity over its width. Figure 4.3 shows thenew optical set-up in PLIF configuration.

ICCD camera

scramjet

Mach 8B nozzle

dump tank

dichroic mirrors

laser beamplano-convex lens

cylindrical lens

test section

Figure 4.3: Optical set-up, PLIF configuration.

A 25 mm focal-length quartz lens (Goyo Optical GMUV42528C) with f / 3.5 aperture was used withICCD camera for PLIF recordings. The ultraviolet signal was filtered using a UG11 filter (Thorlabs).The same exposure time of 300 ns was chosen for the PLIF as for the LIF recordings.


4.2 Scramjet model

The scramjet model that was used in this study consisted of a 3D inlet, a constant area combustor, anda single ramp expansion nozzle. The model is shown in Figure 4.4.

This scramjet model was designed based on the thermal compression concept which was proposed byBillig et al. (1968). Scramjet research has generally tended to focus on two-dimensional or uniformflow fields through the scramjet engine, however, this has led to problems such as high losses due tolarge contraction ratios or engine unstart at off-design conditions. Thermal compression is a methodthat takes advantage of the scramjet engine flow non-uniformities to encourage combustion through-out the entire flow. The present research was done in parallel with another PhD project (Vanyai,2017) which focused on the study of the thermal compression engine. Preliminary numerical work byBricalli et al. (2012) showed promising results for a 3D “Thermal Compression” inlet, which encour-ages strong flow non-uniformity within the combustor. This produces spanwise regions of locally hightemperature and pressure (high compression regions) which ignite the air-fuel mixture. Compressionwaves generated by combustion in such a region propagate throughout the rest of the combustor, ig-niting the flow in regions with low initial temperature and pressure (low compression regions). Thisapproach yields lower mean temperature and pressure, requiring a lower compression ratio and hencelower contraction ratio. As a result, high combustion efficiencies can be achieved (of around 80% inpreliminary CFD), with a reduced risk of engine choking. Demonstrating the capability of thermalcompression will enable much more efficient engine design, i.e., a design of scramjet engines withlow contraction ratios, minimising inlet losses due to compression and combustion losses due to theexpansion of frozen radicals. Subsequently, the risk of thermal choking and unstart due to low meancombustion temperature and pressure is minimised (Billig et al., 1968).

Figure 4.5 shows the 3D inlet with a turning angle that varies in the spanwise direction between 7

and 12.5. Flow approaching the steeper angle must be turned more, resulting in higher compressionin this region compared to that of the lower turning angle. Thus, the intake side with the greater angleof 12 is referred to as the “High Compression” side, and “Low Compression” side for the other. Eachspanwise cross-section is linear, with constant turning angle varying between the two extremes. Thecontraction ratio of the inlet is 3.43.

The combustor had a constant area rectangular channel that was 26 mm high, 75 mm wide and382.6 mm long. On the rear end it was connected to a 198 mm long single ramp expansion noz-zle inclined at 9.2 (top and bottom) to the combustor. The capture area of the intake is 0.00669 m2

and the internal flow path is enclosed by parallel side walls on both sides, resulting in a full-captureintake configuration that does not allow for flow spillage. Both the intake and side walls have sharpleading edges. Measurements were taken on only one side of the engine, close to the bottom of thecombustor, as shown in Figure 4.4. The model was symmetric with regards to the plane of the laser

Section 4.2 Scramjet model 44

InletNozzle

Combustor OpticalWindow

Plenum

179.3 380

754.9

Laser SheetSlot Window

SidePlate

InjectorPlate

26

9

FuelInjectors

Flowdirection

Laser BeamLocation

X

Mounting Rails

Inlet

Nozzle

Combustor

OpticalWindow

MountingStructure

FuelInjectors

Flow

direction

Laser beamposition

Figure 4.4: Scramjet model used for current LIF thermometry experiments (Vanyai, 2017)


Figure 4.5: Isometric view of one half of the intake (Vanyai, 2017).

beam and, thus, the flow should also be symmetrical requiring no need to capture the other side of theengine. The width of the combustor due to orientation of the model becomes the “height” of the LIFimages recorded.

4.2.1 Model position

An optical window has been introduced as the “roof” of the combustor to allow visualisation ofthe LIF experiments. Due to the 3D nature of the flow throughout the scramjet, flow visualisationexamines a plane normal to what is traditionally considered the “vertical” direction, meaning thatthe plane of interest is in the spanwise and streamwise directions. Thus, the model must be rotated90 around the streamwise axis, compared with the traditional orientation of the previous scramjetexperiments. The new orientation is shown in Figure 4.4, along with the structure mounting themodel to the test section rails. Figure 4.6 shows iso contours of pressure from the numerical workof Bricalli et al. (2012). This result shows that most of the combustion occurred in the rear part ofthe combustor. As the OH molecule is an indicator of the combustion process, this means that therear part of the combustor is also the area where sufficient OH signal levels can be detected. Thus,the model was positioned to enable optical access to the rear of the combustor, depending on the areaof the window installed in the scramjet combustor and the location of the window ports in the testsection side walls. In order to ensure that the intake capture area was entirely contained within thecore flow region of the nozzle, the maximum insertion distance of the nozzle into the test chamberwas taken into account as well.

Section 4.2 Scramjet model 46

Figure 4.6: Numerical result for the thermal compression scramjet with φ=0.8 (Bricalli et al., 2012).

4.2.2 Scramjet Model Instrumentation

The scramjet model was instrumented using Kuliter XTEL-190M piezoresistive absolute pressuretransducers to measure surface static pressures inside the engine. The surface static pressure mea-surements were used to provide an indication of whether combustion was occurring in the combustorof the scramjet model. A total of 49 Kulitertransducers were used in the model, in three differentranges: 0 to 68.9 kPa, 0 to 172.4 kPa, and 0 to 689.5 kPa. These pressure transducers were mountedalong the centreline of the model on the bottom internal surface, with the exception of three pressuretransducers mounted on the top internal surface of the intake ramp. On the bottom internal surfacethree transducers were mounted on the intake ramp, 36 inside the combustor, and seven along thenozzle section. Due to the shortage of transducers and amplifier ports not all of the available loca-tions were fitted with transducers. The unused tap holes were blanked off. The transducer leads wereconnected through an instrumentation port in the test chamber floor to external amplifiers, connectedsubsequently to a data acquisition system (DAQ).

4.2.3 Fuel injectors and supply system

The scramjet was fuelled with gaseous hydrogen via eight porthole injectors on the inlet. Theseporthole fuel injectors were located 85.5 mm upstream of the combustor of the scramjet model. Noneof the injectors were at the same height as the other, due to the (constant) gradient in the spanwisedirection. Fuel was injected sonically through orifices inclined at 45 from the local surface normal.The effective flow cross-section covered by each injector was not equal, i.e., the flow rate of airpassing through each spanwise segment was not constant, due to the inlet height being greater atthe high compression side. Therefore, the injector diameters have been scaled to ensure consistentequivalence ratio across all injectors. The diameters were therefore 1.9, 2.0, 2.1 and 2.2 mm from lowcompression to high compression side.

The injectors were supplied with hydrogen via plenum chambers to ensure a uniform fuel-supply


pressure (and hence fuel mass flow rate and equivalence ratio) across all injectors. There were a totalof four plenum chambers in this scramjet model; one for each quadrant of the engine (top high com-pression side, bottom high compression side, top low compression side and bottom low compressionside). Each plenum chamber, which had a volume of approximately 20 cm3, supplied fuel to two port-hole injectors. This design of the plenum chambers was to allow separate fuels and fuelling rates to beused on the low and high compression sides of the injector plate, for example, in the study by Vanyai(2017). For the present study, all plenums provided with the same hydrogen fuel and same fuel-supplypressure. Each of the four fuel plenums was instrumented with a single PCBr piezoelectric pressuretransducer of range 0 to 3448 kPa for the measurement of plenum pressure for the computation of fuelmass flow rate.

Two Ludwieg tubes, external to the facility test section and connected to the model with rigid stainlesssteel fuel piping, were used to provide a constant fuel supply to the four plenum chambers during theexperiments. Each Ludwieg tube was connected to two plenums on either the high or low compressionside of the model. This was done to provide the possibility of different fuel types and fuelling rateson both sides, as explained previously.

T4 test section

Fast-actingsolenoidBvalve

LudwiegBtubepressureBgauge

LudwiegBtubefillBvalve

H2BgasbottleLudwiegB

tube1/2BinchBtubing 5/8BinchBtubing

TopBhigh-compressionBsideBplenumB

chamber

BottomBhigh-compressionBsideBplenumB

chamber

LudwiegBtubepressureBgauge

LudwiegBtubefillBvalve

H2Bgasbottle

LudwiegBtube

5/8BinchBtubing

Fast-actingsolenoidBvalve

1/2BinchBtubing

TopBlow-compressionBsideBplenumB

chamber

BottomBlow-compressionBsideBplenumB

chamber

Figure 4.7: Schematic of the fuel delivery and injection system for T4 LIF experiments

Section 4.3 Test conditions 48

A fast-acting ASCO-JOUCOMATIC solenoid valve (SCB223A103) was mounted in-line connectingthe plenum chambers and the Ludwieg tubes. This valve was used to initiate the flow of the fuel tothe injectors; with the valve triggering time adjusted to ensure steady plenum pressures during the testtime. This ensured that a constant fuel mass flow rate (and hence a constant equivalence ratio) wasmaintained during the test time. From calibrations of the fuel system conducted prior to the scramjetexperiments, it was determined that the fuel system required approximately 12 ms before a steadyfuel-supply pressure can be attained. Figure 4.8 shows the fuel timing relation to the test time from arepresentative test in this experimental campaign.

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Figure 4.8: Fuel injection timing during a LIF experiment

For all tests conducted for the present study, the total equivalence ratio φ provided by the eight injec-tors was approximately 0.8±0.1. This value for equivalence ratio was chosen to ensure combustionoccurred on both high and low compression sides of the scramjet engine, which then allowed sufficientsignal levels of hydroxyl fluorescence. The value of equivalence ratio was also chosen to ensure thescramjet model did not unstart from thermal choking during the test time. An unstart in the scramjetmodel would cause damage to the ICCD camera due to overexposure.

4.3 Test conditions

The experiments were conducted at a test condition which simulated a scramjet-propelled vehicleflying at Mach 9.7 at an altitude of 30 km (which equates to a flight dynamic pressure of 77 kPa).This assumes that the scramjet model is 80% scale of the actual flight vehicle and that the scramjet islocated downstream of a 7 forebody wedge on the vehicle. In order to achieve this test condition, theT4 shock tunnel facility was operated with the fill conditions specified in Table 4.1.


Table 4.1: Nominal shock tunnel filling conditions.

pST TST pRES pCT CT mixture

192 kPa 300 K 6 MPa 80.5 kPa 70%Ar + 30%He

For the present study, a total of 42 repeat tests were conducted. Average values of the test conditionsfrom these 42 repeat tests, along with the measurement uncertainties and repeatability, are reported inTable 4.2.

Table 4.2: Nozzle-supply conditions (subscript s) and test conditions at the exit of the nozzle (subscript ∞).The estimated species mass fractions X at the nozzle exit plane are also shown.

Parameter Unit Value Uncertainty Repeatability

ps MPa 46.21 ±3% ±3%Ts K 3751 ±5% ±3%hs MJ/kg.K 4.61 ±7% ±2%

p∞ kPa 3.96 ±13% ±17%T∞ K 384.7 ±11% ±7%u∞ m/s 2919 ±4% ±3%rho∞ kPa 0.0358 ±12% ±12%M∞ - 7.4 ±3% ±0.8%

XN2 - 0.717 - ±0.6%XO2 - 0.188 - ±3%XAr - 0.01286 - > 0.01%XO - 0.0004 - ±28%XNO - 0.08174 - ±11%

The test conditions were calculated by first computing the nozzle-supply conditions (reported in Ta-ble 4.2 as variables with subscript s) using the equilibrium shock tube condition calculator ESTCj (Ja-cobs et al., 2011). The measured incident shock speed in the shock tube and nozzle-supply pressureps were used as inputs to ESTCj. Note that due to the extremely high temperatures and pressures inthe nozzle-supply region, thermal and chemical equilibrium were assumed in these calculations. Thecomputed nozzle-supply conditions were then used as inputs to a non-equilibrium nozzle conditioncalculator NENZF (Lordi et al., 1966) for the estimation of test conditions at the exit of the facilitynozzle. In NENZF, the test conditions were computed by performing a quasi-one-dimensional ex-pansion of the nozzle-supply conditions using using curve-fits to thermo-chemical models to match aPitot-to-nozzle-supply pressure ratio of 0.006. The value of Pitot-to-nozzle-supply pressure ratio wasobtained from a Pitot pressure survey of the uniform flow region at the exit of the Mach 8B supersonicexpansion nozzle of the T4 facility.

The uncertainties of the test conditions in Table 4.2 were computed following the method by Mee

Section 4.4 Experimental Data Reduction: Test time and surface pressure 50

(1993). Also shown in Table 4.2 is the repeatability of the test conditions, which was calculated usingthe Student t-estimator at 95% confidence interval for a sample size of 42. It is noted here that themeasurement uncertainties for most flow properties (except the freestream static pressure p∞) werehigher than the repeatability of the 42 tests.

4.4 Experimental Data Reduction: Test time and surface pres-sure

The data acquisition system (DAQ) used in this study consisted of 12 National Instruments NI-PXI-6133 cards with effective sampling rates of 2.5 Msamples/s. The start of data acquisition on the DAQsystem was triggered by a rise in the voltage output from one of the two transducers measuring thepressure in the nozzle-supply region. The DAQ system was also used to trigger the optics system - theNd:YAG laser was triggered by a rise in the measured nozzle-supply pressure, and the ICCD camerawas triggered 300 ns after the Nd:YAG laser pulse. In addition, the DAQ system was also used toactivate the fast-acting solenoid valves to initiate fuelling in the engine.

4.4.1 Test time determination

It was mentioned earlier in this chapter that the nature of the impulse facilities limited test times toseveral milliseconds. The test time was defined as a period of time during which quasi steady flow wasestablished in the facility nozzle and over the model. Both flow in the nozzle and over the model needtime to develop. This hypersonic nozzle is started after the period of initial unsteady expansion, andindicated by the constant ratio of Pitot pressure and nozzle-supply pressure. The flow over the modelstarts to establish at the moment when the flow reaches the model leading edge. A study by Jacobset al. (1992) showed that the model establishment time can be correlated with a number of flow-over-model lengths, and found approximately three lengths to be required for the turbulent boundarylayers to be fully developed. For the current study, the facility nozzle start-up time and model flowestablishment time was estimated to be 1.8 ms. This is indicated as period (a) in Figures 4.9 and4.10. The time trace in Figure 4.9 is the nozzle-supply pressure measurement from a representativetest in the current study , while the time trace in Figure 4.10 is representative of a static pressuremeasurement in the vicinity of the axial location where LIF measurements were taken. The test timewindow of approximately 0.7 ms was taken to start at the end of period (a) shown in the Figures 4.9and 4.10, and to end when the nozzle-supply pressure decreases by more than 5% of the nominalnozzle-supply pressure level. This is denoted by period (b) in Figures 4.9 and 4.10.

One of the issues with testing in high-enthalpy impulse facilities is the possibility of contamination ofthe test gas with driver gas. In a T4 study using mass spectroscopic measurements, Boyce et al. (2005)found the following empirical correlation for contamination time, with 10% driver gas contamination:


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Figure 4.9: A time trace of the nozzle-supply pressure measured for test 11607. Flow establishment time andtest time windows are indicated.

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Figure 4.10: A time trace from a static pressure measurement taken in the vicinity of the axial location whereLIF measurements were taken (test 11607). Flow establishment time and test time windows are indicated.

Section 4.5 Summary 52

τ10% = 62.129 · h−1.7183s ± 38% (4.1)

where hs is the nozzle-supply (stagnation) enthalpy in MJ/kg and τ10% is the contamination time inmilliseconds.

For the present study, this correlation estimates that it takes 4.5±38% ms for the test gas to be con-taminated with 10% of driver gas. For the selected test time window in Figures 4.9 and 4.10, it isclear that there was less than 10% driver gas contamination in the test gas.

One thing must be noted here - as laser-induced fluorescence measurements were taken within a timeframe that was an order of magnitude lower than the determined test time, it was easier to find a“slice” of time for LIF measurements within the determined steady state period. In the present study,LIF images were recorded 2.5 ms after the shock reflection in the nozzle supply region (Figure 4.10)and each image was recorded during 300 ns.

4.4.2 Surface pressure measurements

When repeating tests in the T4 shock tunnel facility, it is typical to get variations in the test conditionsbetween each test. These variations in test conditions cause variations in flow conditions in the scram-jet model. For the present study, variations in surface static pressure measurements in the scramjetmodel, which brought about variations in test conditions, were apparent in the 42 tests conducted. Toreduce the effects of test-to-test variations brought about by variations in test conditions, it is commonpractice to present surface pressure measurements as values normalised by the nozzle-supply pressureps for each test. As such, the surface static pressure distribution shown in Chapter 6 are all presentedas normalised values.

4.5 Summary

The experiments in this research were conducted in the T4 free piston shock tunnel facility at The Uni-versity of Queensland, with the new experimental optical diagnostic arrangement to implement theLIF, PLIF and emission spectroscopy methods. For these experiments a thermal compression scramjetmodel was used. Present Chapter provided descriptions of the facility, test model and optical arrange-ments for LIF, PLIF and emission spectroscopy. Information on the model position, instrumentationand fuelling was given. Test conditions were reported and test time was determined. Surface pressuremeasurements will be presented as normalised values to reduce the effects of test-to-test variationsbrought about by variations in test conditions.

Chapter 5

Calibration of LIF setup

The new experimental optical diagnostic system for the LIF, PLIF and emission spectroscopy methodsthat was added to the capabilities of the T4 facility was described in Chapter 4. This system had tobe calibrated, i.e., tested on a simpler experiment before it was used for more complicated scramjetcombustion measurements.

The new LIF set-up was calibrated with the atmospheric H2 flame experiments. These experimentswere done in both one-and two-dimensional form. Spectrally resolved measurements were obtainedwith the same LIF set-up described in Chapter 4. The test section and shock tube were moved, anda H2 torch (Bernzomatic TS4000) was placed at the location where the scramjet is located duringshock tunnel experiments, as shown in the Figure 5.1. The ultraviolet signal was filtered using a UG5and two WG305 filters. Four different excitation lines were probed, Q1(8), Q1(9), P1(2) and R2(13).Experiments were done with two different positions in the flame, one on the left side of the flame andthe other through the middle of the flame. Two equivalence ratios were used for both positions andall the excitation lines. Figure 5.2 shows an example of results at these two different positions for thesame equivalence ratio. An exposure time of 70 ns was chosen and reported results were obtained byaveraging 500 images. Table 5.1 gives information on each experiment. Flame height was measuredto be 90.29 mm.

Figure 5.3 shows the saturation curve generated using the new LIF system at approximately 1 atm.The laser power was the maximum power, corresponding to the non-linear part of the saturationcurve. The maximum power was chosen in order to maximise the OH fluorescence signal and thusto maximise detection sensitivity. Because the signal in the saturation regime becomes independentof the laser irradiance and the electronic quenching, another benefit of saturated LIF is that it enablesavoiding the quenching corrections .

Section 5.0 54

laser beamdichroic mirror

test section

support beams

Mach 8B nozzle

shock tube

(P)LIF box

Flame

Torch

Figure 5.1: Flame experiments setup.

Figure 5.2: PLIF images for Q1(8) at different positions in the flame, φ=0.3.

Chapter 5 Calibration of LIF setup 55

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0 0.2 0.4 0.6 0.8 1 1.2 1.4

LIF

sig

nal [

coun

ts]

Photodiode reading [V] (Laser energy)

Flame LIFExponential fit

Figure 5.3: Saturation curve.

Table 5.1: Flame experiments. Laser position 1 (LP1) is at the left side of the flame, while laser position 2(LP2) is through the middle of the flame.

EXP # Laser position Spectral line φ

1 LP1 Q1(8) 0.3

1_2 LP2 Q1(8) 0.3

2 LP1 Q1(8) 0.2

2_2 LP2 Q1(8) 0.2

3 LP1 R2(13) 0.3

3_2 LP2 R2(13) 0.3

4 LP1 R2(13) 0.2

4_2 LP2 R2(13) 0.2

5 LP1 P1(2) 0.3

5_2 LP2 P1(2) 0.3

6 LP1 P1(2) 0.2

6_2 LP2 P1(2) 0.2

7 LP1 Q1(9) 0.3

7_2 LP2 Q1(9) 0.3

8 LP1 Q1(9) 0.2

8_2 LP2 Q1(9) 0.2

Section 5.1 Flame experiments results and discussion 56

5.1 Flame experiments results and discussion

Figure 5.4 to Figure 5.11 show the comparison of each flame experiment with the three syntheticspectra simulated at 3000 K and also a comparison between two corresponding flame measurements.

As an example flame experiment with Q1(8) excitation line is taken, shown in the Figure 5.4. Thisexperiment was done at the first laser position (left side of the flame), and with two different fuelequivalence ratios. Each equivalence ratio result was compared with the three synthetic spectra simu-lated at 3000 K and these two different equivalence ratio results were then compared to each other. Itis clear from the figure that none of the two cases of this example experiment is in agreement with thesynthetic spectra. The flame experiment results are reflections of the OH concentrations that are notin thermal equilibrium. In Figure 5.4 the fluorescence spectra are dominated by two strong transitionsQ1(8) and R1(7) originating from the laser-excited level. Another transition also originating fromthe laser-excited level would be P1(9) at about 318.14 nm, not seen in this figure due to the fact thatwavelengths longer than 317 nm were not captured. The levels of other transitions are much lowerthan both the levels of the same transitions in the synthetic spectra, and the laser-coupled transitionlevels in these experimental spectra. The fact that laser-coupled transition are dominating the spec-tra and other transitions are at much lower levels is a proof that both the vibrational and rotationalrelaxation occurred only partially. In the case of complete relaxation transfer of population to levelsother than the ones directly coupled with the laser-excited level would be complete and experimen-tal spectra would be in agreement with the synthetic spectra. The level of agreement between thesespectra would then be dependant on the temperature difference (except the slight differences in themodelling). Thus, by changing the temperature of the simulation and comparing the resulting spectrawith the experiment, once when the agreement between the spectra is achieved it would be possibleto determine the temperature in the experiment.

All of the presented flame experimental results show qualitatively the same behaviour described inthe the example.

The comparison with thermalised spectral simulation results showed a significant discrepancy be-tween the synthetic spectra and the flame experimental spectra, indicating that the OH concentrationsare only partially thermalised. The conclusion is that a non-equilibrium spectral simulation is neces-sary in order to have a proper comparison and a possibility of a better agreement with the experimentalspectra. For that purpose LIFBASE is used, due to its ability to adjust the populations of the indi-vidual vibrational and rotational levels, thus enabling a full simulation of the laser pumping for theQ1(8) transition. In order to obtain temperature distribution along the flame height each LIF imagewas divided into 10 blocks or sections (Figure 5.12). Sections are counted from the bottom of theimage towards the top. Each section provides one OH LIF spectra and was evaluated separately in thenext chapter, resulting in one temperature per section.


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Figure 5.4: Flame experiments for Q1(8) at first laser position.


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Wavelength, λ [nm]

Q1(8)

LP1,φ=0.3LP1,φ=0.2

Figure 5.5: Flame experiments for Q1(8) at second laser position.


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R2(13)

LP1,φ=0.3LP1,φ=0.2

Figure 5.6: Flame experiments for R2(13) at first laser position.


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R2(13)

LP1,φ=0.3LP1,φ=0.2

Figure 5.7: Flame experiments for R2(13) at second laser position.


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LP1,P1(2),φ=0.3LIFBASE

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P1(2)

LP1,φ=0.3LP1,φ=0.2

Figure 5.8: Flame experiments for P1(2) at first laser position.


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P1(2)

LP1,φ=0.3LP1,φ=0.2

Figure 5.9: Flame experiments for P1(2) at second laser position.


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Q1(9)

LP1,φ=0.3LP1,φ=0.2

Figure 5.10: Flame experiments for Q1(9) at first laser position.


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Q1(9)

LP1,φ=0.3LP1,φ=0.2

Figure 5.11: Flame experiments for Q1(9) at second laser position.


Figure 5.12: PLIF image for Q1(8) at first laser position, φ = 0.3 divided in sections. Sections are counted fromthe bottom of the image towards the top.

5.1.1 Non-equilibrium spectral simulation

The process was iterative, changing several significant parameters until satisfactory agreement ofthe synthetic and experimental spectra was obtained. The controlling parameter was the R2 value,where R2 is the coefficient of determination. The maximum value of R2 corresponds to the optimumvalues of the fitting parameters and thus, of the spectral match. First, the rotational distribution withinv′ = 1 was varied for a certain temperature until the simulated spectrum was judged to be in the bestagreement with the experimental one, with the R2 as the controlling parameter. The majority ofthe population was placed in the laser pumped rotational level, N′ = 8, while the rest of the rotationallevels were left to follow Boltzmann distribution, thus defining a temperature. Second, the partitioningbetween the F1 and F2 spin components had to be varied as well. The fitting was started by keepingall the population in the excited spin orbit level (v′ = 1, F1 in this case). However, F2 needs to beincluded to improve the fit (generally adding about 20-30% population in that spin orbit, dependingon the LIF image section). For instance, for the fully thermalised case at combustion temperature of2000 K, the percentage of F1 and F2 is 54.7% and 45.3%, respectively. Third, the distribution of thevibrational levels was adjusted, placing the majority of the population in the v′ = 1 vibrational level.The population of the vibrational levels was varied and adjusted, and the whole procedure repeateduntil the optimum spectral agreement was achieved. The described fitting procedure was done for arange of temperatures, with the highest value of R2 in total corresponding to the rotational temperaturein the experiment, for that specific section of the LIF image. The analysis was repeated for all of the10 sections of a LIF image. Thus, the temperature distribution along the flame height is obtained


at the laser position in the experiments. The temperature distributions along the flame height wereobtained for two positions within the flame. From Figure 5.15 it is evident that there is a unique peakR2 value which can be used to derive temperature. The uncertainty of the derived temperature wasthen assumed to be the temperature resolution at which the LIFBASE spectra were generated at. Forthe example in Figure 5.15 the derived temperature is 2100±100 K.

Figure 5.13 is example of the obtained best fit and Figure 5.14 of the corresponding rotational distri-bution for a section of a LIF image. This distribution is dominated by the initially pumped level Q1(8)but shows that RET has occurred only partially. For the spectrum of section # 1 in Figure 5.13, about33% of the total v′ = 1 population is found in N′ = 8, and the remaining 67% is distributed amongother levels in a roughly 2100 K Boltzmann distribution, however, about 82% of the total populationis retained within the F1 component even when RET has taken place. This approach assumes that therotational levels surrounding N′ = 8 have already equilibrated and thus follow a Boltzmann popula-tion distribution. Figure 5.16 shows an example of an obtained temperature distribution in the flame,achieved for the experiment with Q1(8) excitation at laser position left and φ = 0.3.

An interesting phenomenon was found during the analysis of the flame results: the described fittingprocedure was possible for the results were the excitation line was a Q line, irrelevant of the J-number.It was not possible to achieve the same results when the fitting method was applied to the LIF datawhere excitation was by a R line (Figure 5.17). The reason for this remains unclear, however it isimportant to note when choosing an excitation line for future experiments, whether in a flame or ina scramjet. When the excitation was by a P line, the fitting was essentially possible, as shown in theFigure 5.18. However, except for the sections closest to the burner, the temperature value were farbelow from what is expected in a flame (below 1000 K), shown in the Figure 5.19. The reason forthis is most likely the very low signal achieved in these experiments, an order of magnitude lowerthan for the experiments with Q excitation line. Similar biasing of the results due to low signal levelswere previously observed by Neuber et al. (1996). Thus it was considered that the present resultsachieved by a P excitation line were erroneous due to low signal, i.e., insufficient OH present in themeasurement volume, and therefore were excluded from comparison with Q line fitting results.

In previous flame studies complete rotational relaxation to a thermal distribution has not been ob-served for either atmospheric flames or low pressure flames (Doherty and Crosley, 1984; Stepowskiand Cottereau, 1981). In the experiments with H2/N2O flame (Jeffries et al., 1988) excited N′ = 3,N′ = 8 and N′ = 16 and reported that each of the initially excited N’ showed distinctly different rota-tional distribution. The fluorescence originating from the initially pumped level was 33%, 36% and38% for N′ = 3, N′ = 8 and N′ = 16, respectively, while for the H2/O2 flame with N′ = 8 excited, 38%of the fluorescence originates from the initial level. These results are consistent with the 33% of thefluorescence from the laser excited level in the present study.


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Flame EXP1LIFBASE best fit

Figure 5.13: Experimental spectrum fitted to LIFBASE spectrum. Spectra normalized to the same area.

0 5 10 15 20

Rot

atio

nal p

opul

atio

n

Rotational level

Figure 5.14: Rotational population distribution for sec # 1, flame EXP1.


0.86

0.88

0.9

1000 1600 2200 2800

R2

Temperature [K]

Figure 5.15: Coefficient of determination R2 for section # 1, flame EXP1.

Upper rotational levels, other than the directly excited one, are populated only by rotational relaxationprocesses out of the directly populated level, because at, or near saturation conditions, collisionalexcitation is completely negligible (Lucht and Laurendeau, 1979). Hence, the rotational distributionin the upper levels is independent of irradiance. The ratio of populations in levels populated by RETand directly excited level is determined by the rates of rotational relaxation and electronic quenchingin the upper levels. As electronic quenching is no longer balanced by the collisional excitation, theupper levels populated by RET will be underpopulated with respect to the directly excited level inthe general case. Only in the case where the ratio of RET and quenching is very large (> 102) willthe populations in the upper rotational levels follow approximate Boltzmann distribution (Lucht andLaurendeau, 1979).

5.1.2 Multi-line thermometry: Boltzmann plot

The temperature profile obtained with the non-equilibrium distribution method was verified with thetemperature profile obtained with the well-established multi-line thermometry approach. This fluo-rescence technique is utilised to generate one-dimensional temperature distribution along the flameheight. First, a brief theoretical background to the multi-line technique is given.

The imaged fluorescence signal, i.e., the number of detected photons (Palma, 1999) is

S = NT fBB12EgnΦFΩ

4πηopt l (5.1)


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ht [m

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non-thermal distribution

Figure 5.16: Temperature distribution in flame for EXP1.


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Figure 5.17: Experimental spectrum fitted to LIFBASE spectrum.Spectra normalized to the same area.

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Figure 5.18: Experimental spectrum fitted to LIFBASE spectrum. Spectra normalized to the same area.


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non-thermal distribution

Figure 5.19: Temperature distribution in flame for EXP5.


It is assumed that the same optical system is used for all measured transitions, hence, the opticalefficiency ηopt , the measurement volume (V = l · a) and the solid angle Ω / 4π influence both mea-surements to the same degree and do not need to be determined. The collected fluorescence signal S

is a function of temperature through the Boltzmann fraction fB which can be written as

fB =Ni

NT(5.2)

fB =2J′′+1

Ztot· e( −FJ′′

kBTrot

)· e( Gv′′

kBTvib

)(5.3)

where J′′ is the rotational quantum number in the electronic ground state, Gv′′ the vibrational energyand FJ′′ the rotational energy of the lower state ′′. Tvib is the vibrational and Trot the rotational temper-ature. The total partition function is denoted Ztot . It is assumed here that the molecule is in its groundstate where the electronic energy is zero.

S = NT2J′′+1

Ztot· e( −FJ′′

kBTrot

)· e( Gv′′

kBTvib

)B12EgnΦF

Ω

4πηopt l (5.4)

If the ground state of all the probed transitions is the same vibrational, but different rotational level,then the vibrational energy contribution is constant. Thus this term and all the J-independent quanti-ties that are considered constant for different transitions cancel out in the Equation 5.4.

S ∝(2J′′+1

)B12 e

( −FJ′′kBTrot

)(5.5)

Rearranging the formulation gives

ln(

SSJ′J′′ (2J′′+1)

)(5.6)

which plotted against FJ′′ produces a straight line with slope -1/kBTrot . This plot is termed Boltzmannplot. In the expression the Einstein coefficient for stimulated absorption B12 is replaced with therotational line strength factor (Hönl-London factor) SJ′J′′ . Tvib can be determined assuming that thesame rotational levels, but different vibrational levels are excited where the Einstein coefficient forstimulated absorption B12 is replaced with the vibrational line strength factor (Franck-Condon factor)FC. Table 5.2 provides details on the spectroscopic constants used in this method. For the multi-linemethod each image was divided in 10 sections. The area under spectrum in each image was computedto get a signal value S used in the formerly stated equations.


Table 5.2: Parameters of spectral lines used for the OH multi-line thermometry experiments.

Spectral v′′ ν0 FJ′′ SJ′J′′

line [cm−1] [cm−1]

Q1(8) 0 35256.42 1484.2 0.936Q1(9) 0 35210.64 1829.9 0.946P1(2) 0 35377.79 162.03 0.531R2(13) 0 35340.31 3555.1 0.474

Uncertainty analysis for multi-line thermometry

As the temperature was presented in the form of distribution through the combustor, where the LIFimages were divided in 10 sections, the same approach was followed here. The subsequent equationsare for each of the 10 sections of a LIF image. The basis for the uncertainty analysis is the expression

Trot ∝−FJ′′/kB

ln(

SSJ′J′′(2J′′+1)

) (5.7)

It is assumed that spectroscopic constants are known exactly and thus do not contribute to the un-certainty. The uncertainty is then calculated as error in the recorded signal. Writing the expressionas

Trot ∝−FJ′′/kB

ln(

SiSJ′J′′(2J′′+1)

) =C1

C2(5.8)

then the partial derivative of Trot with respect to a signal Si is (O’Byrne, 2002)

∂Trot

∂Si=−C1

SiC22

(5.9)

The uncertainty ∆Trot [K] of the temperature Trot [K] due to variations in the recorded fluorescencesignal Si is then given as

∆T Trot =

√∑

i

(∂Trot

∂Si∆Si

)2

(5.10)

where ∆Si is the uncertainty of the recorded fluorescence signal. The uncertainty ∆Si [counts] of therecorded signal Si [counts] is evaluated using


∆Si =

√1

z−1

z

∑j=1

(S j−Savg

)2 (5.11)

where the number of images recorded at that transition is represented by z and the average signal Savg

is given by

Savg =1z

z

∑j=1

S j (5.12)

Each of the 500 images was divided in 10 sections. The area under spectrum in each image wascomputed. Equation 5.12 gives an average of 500 of these areas (signals) for each section of animage.

Figure 5.20 and Figure 5.21 show the computed temperature distribution compared with the non-equilibrium distribution method (fitting procedure) for the left and middle position within the flame,respectively. As mentioned earlier, the fitting method produced temperature results only for the ex-periments where the excitation line was a Q line. The computed uncertainty for the multi-line methodwas rather small (±<1 K), yet not surprising, when taken into account that this is the uncertainty dueto signal fluctuations only. As each result is an average of 500 images, and each section’s spectrum isan average of a number of pixel rows, the signal fluctuations are well averaged out, resulting in smalluncertainty.


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burner side

non-equilibrium distr.; Q1(8)non-equilibrium distr.; Q1(9)

multi-line thermometry

Figure 5.20: Comparison of temperature distributions in flame; position left.


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multi-line thermometry

Figure 5.21: Comparison of temperature distributions in flame; position middle.


5.2 Summary

The LIF setup was tested and calibrated with atmospheric H2 flame experiments. The comparisonwith thermalised spectral simulation results showed that there is a large discrepancy between theLIF flame spectra and synthetic spectra. The conclusion was that the flame OH concentrations wereonly partially thermalised. Thus, a non-equilibrium spectral simulation was used in order to have aproper comparison and a possibility of a better agreement with the experimental spectra. By fittingthe LIFBASE spectra to the flame experimental spectra, a very good agreement of the synthetic andexperimental spectra was achieved. The best fit corresponds to the optimum values of the fitting pa-rameters and thus, of the spectral agreement. The main fitting parameters were temperature, speciesconcentration and spin-orbit combination factor (the partitioning between the F1 and F2 spin compo-nents). The fitting was done for a range of temperatures, and the best fit used to find the rotationaltemperature in the experiment, for that specific section of the LIF image. The analysis was repeatedfor all of the 10 sections of a LIF image, thus obtaining the temperature distribution throughout theflame at the laser position in the experiments. The temperature distributions along the flame heightwere obtained for two positions within the flame and two excitation lines (Q1(8) and Q1(9)). Therewere some discrepancies between the results for different excitation lines, possibly due to differencesin LIF signal recorded.

These results were verified with the temperature profile obtained with the well-established multi-line thermometry approach. The comparison shows good agreement between these two thermometrytechniques. The discrepancies may be attributed to the differences between the synthetic spectra con-stants and the experimental ones, the multi-parameter fitting and differences between the thermometrymethods approach.

Chapter 6

Scramjet Combustion Experiments

The laser-induced fluorescence experiments were performed in a scramjet to obtain the temperaturedistribution through the combustor. The results bring new resources which can be further used inoperational scramjet engines, i.e., hypersonic vehicles. The results presented here were obtainedeach from a single run of the shock tunnel. Given the environment in which these experiments wereperformed (turbulent, supersonic combustion and LIF data is time-resolved within few nanoseconds)it is the most accurate approach to analyse each tunnel run data separately, rather than averagingacross multiple tests.

6.1 OH LIF Thermometry Measurements

Specific transition within the A2Σ+ - X2Π (1,0) band of OH is selected for the laser excitation on thebasis of several criteria: its isolation from neighbouring lines, the temperature sensitivity associatedwith its use in measurements, and the expected LIF signal based on its lower level population fractionsat rotational temperatures present in the combustion. The minimum separation between spectral fea-tures necessary to fulfil the first of these criteria is approximately 1 cm−1, a requirement satisfied bymany lines in the (1,0) band of OH (Palmer and Hanson, 1995), as shown by theoretical LIF spectrumin Figure 6.1 generated with LIFBASE. The transition selected for this study is the Q1(8) transition ata wavelength of 283.55 nm. This line was used in previous studies (McGuire, 2007; O’Byrne et al.,2005), where it was found that this transition line produces strong fluorescence signal and is relativelyinsensitive to variations in temperature. In the environment where there are large temperature fluctua-tions, like a scramjet combustor, it is important to maintain strong signal for a range of temperatures.In the temperature range from 1300 - 3300 K the intensity of the Q1(8) line for a given pressure variesby less than 25%. Figure 6.2 shows the variation in signal strength generated with LIFBASE overthis temperature range, confirming the weak temperature dependence of the signal strength for Q1(8)transition line.

Chapter 6 Scramjet Combustion Experiments 79

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Figure 6.1: Theoretical LIF OH spectrum at 1 atm and 3000 K.

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Sig

nal s

tren

gth

[%]

Temperature [K]

Figure 6.2: Variation of the Q1(8) transition fluorescence signal with temperature, generated with LIFBASE.

Section 6.1 OH LIF Thermometry Measurements 80

Figure 6.3: Laser-induced fluorescence image. Sections in the image on the right are counted from the bottomof the image towards the top.

6.1.1 LIF results

Figure 6.3 shows an example of a LIF image obtained in scramjet combustion experiments. The imagesize is 1024 x 1024 pixels, where the horizontal pixels correspond to the wavelength observed andvertical pixels to the width of the combustor. The objective is to obtain spatially resolved temperaturemeasurements, and ideally that would result in each horizontal row of pixels (1024 rows) giving onetemperature. However, it would be very difficult to generate one spectrum for every horizontal row ofpixels because of the low signal-to-noise ratio, SN. Thus an image is divided into a specific number ofblocks or sections and averaging of pixel rows is done, as shown on the right image of Figure 6.3. Thenumber of sections depends on the SN ratio in each section and this division results in one spectrumfor each section, i.e., one temperature measurement for each section. To find the optimal number ofsections for these LIF images, an investigation was performed varying the number of sections andcomputing SN ratio for each of the sections. Signal-to-noise ratio was computed as

SNi = Siav/σi (6.1)

where SNi is the signal-to-noise ratio for a section i, Siav is signal intensity averaged for section i,

and σi is the standard deviation of section i. Some of the results of this investigation are presented inTable 6.1. Based on these data, it was chosen to continue with ten sections for further data analysis.

Figure 6.4 represents the spatial intensity distribution, i.e., intensity distribution over the combustorwidth. It can be seen that higher intensity is observed in the lower part (high compression side) of thecombustor. Higher intensity, i.e., higher signal from laser-induced OH fluorescence, means that thereis more OH created in this energy level, and due to temperature invariance, more combustion in thatregion of the combustor. This is consistent with the thermal compression concept that predicts morecombustion on the high compression side of the engine.


Table 6.1: SN ratios for several different numbers of sections of a LIF image.

Number of sections

Sec # 3 5 8 10 12

1 0.9017 0.6754 0.4331 0.3318 0.2587

2 0.4961 1.0886 1.1519 0.9963 0.8719

3 0.2500 0.4303 1.0925 1.2500 1.2334

4 0.2743 0.5692 0.9142 1.1705

5 0.2576 0.3155 0.5481 0.7635

6 0.2386 0.3007 0.5468

7 0.3088 0.3153 0.3107

8 0.2158 0.2158 0.3263

9 0.3235 0.1825

10 0.1817 0.2949

11 0.3181

12 0.1582

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60

70

0 20 40 60 80 100 120 140

Com

bust

or w

idth

[mm

]

Intensity [a.u.]

Figure 6.4: Spatial intensity distribution.


Figure 6.5 is a representative OH spectrum extracted from a section of a LIF image. Sections arecounted from the bottom of the image towards the top. In Figure 6.6 spectra from all ten sectionsare shown. Figure 6.7 shows the relative standard deviation for each of the sections, while Figure 6.8shows sections’ signal-to-noise ratio.

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Figure 6.5: Example of spectrum in a section.

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123456789

10

Figure 6.6: Spectra in all 10 sections.

Intensity ratio

The objective of this study is to obtain temperature from the thermally-assisted laser-induced fluo-rescence. This means that the temperature should be extracted from the bands that are populated by


75

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85

90

95

100

105

110

1 5 10

(Sta

ndar

d de

viat

ion)

/(M

ean)

*100

[%]

Section number

Figure 6.7: Relative standard deviation in all 10 sections for test # 11607.

0

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0.6

0.8

1

1.2

1.4

0 2 4 6 8 10

S/N

rat

io

number of sections

Figure 6.8: S/N ratio in all 10 sections for test # 11607.


the molecular energy transfer, including RET and VET, after the excitation of Q1(8) in the 1-0 band.Figure 6.9 shows the processes following the Q1(8) (283 nm) excitation.

It can be seen in Figure 6.9 that, within the wavelength area focused on with the spectrometer(around 300 - 320 nm), R(V)ET populated vibrational bands are 0 - 0 and 2 - 2. The rotational lev-els of the excited state (A-state) are expected to be thermalised (Neuber et al., 1996), and it shouldbe possible to deduce the temperature purely from the rotational spectra of the individual vibra-tional bands. Figure 6.10 shows the section intensity ratios for different rotational lines for theshock tunnel test # 11607. The first plot is the 0 - 0 band 306.8 nm / 309.1 nm intensity ratio whichis essentially an intensity ratio between rotational levels with quantum numbers N ≈ 8-12 (around306 nm) and ≈ 1-5 (around 309 nm). Also shown are ratios 319.8 nm / 321.1 nm, 320.8 nm / 321.9 nmand 320.6 nm / 321.5 nm intensity ratios in the 2-2 band which correspond to the intensity ratiosQ1(2) / Q2(5), Q1(6-7) / P1(5) and Q1(5-6) / Q2(7), respectively.

In order to extract temperature from these intensity ratios, a comparison with the synthetic spectrawhere temperature is known was made. This was done according to the following procedure:

• Experimental intensity ratios were computed for each section for several different rotationallines

• Synthetic intensity ratios were computed with LIFBASE, SPARTAN and Photaura for the samerotational lines and for a range of temperatures 1000 - 4000 K, with ∆T = 100 K

• Each experimental intensity ratio was compared to the corresponding (same rotational lines)synthetic intensity ratios from spectra at different temperatures, until the same synthetic inten-sity ratio was found

• Synthetic spectra of that matching synthetic intensity ratio and at a certain temperature wereplotted together with the experimental spectra

• If the synthetic spectra and experimental spectra are a match, then the conclusion is that theexperimental spectra corresponds to the same temperature as the synthetic spectra

Figure 6.11 shows an example of the results obtained with the described procedure for spectra fromone section. It is clear that even though the intensity ratios of the experiments and the spectral sim-ulations are in agreement, the spectra are not. In all three plots there is a significant departure ofthe experimental results from the simulations. Due to the fact that spectral simulation results arerepresentative of the completely thermalised case, it is easy to conclude that the experimental spec-tra is thermalised only to some degree and not fully. This shows that the assumption of completelythermalised rotational levels of the excited state (Neuber et al., 1996) is not valid here.


VE

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Figure 6.9: Q1(8) excitation.


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Figure 6.10: Peak intensity ratio for different rotational lines for the test # 11607.


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Figure 6.11: Comparison of synthetic spectra with LIF for the same intensity ratio. LIF data obtained withQ1(8) laser-excitation. Normalized to the maximum intensity value. Instrumental broadening (apparatus func-tion) set at 0.25 nm for all spectra.


6.1.2 Non-equilibrium spectral simulation

The comparison with thermalised spectral simulation results showed a significant discrepancy be-tween the spectra, and that the experimental OH concentrations are only partially thermalised. Theconclusion is that a non-equilibrium spectral simulation is necessary in order to have a proper com-parison and a possibility of an agreement with the experimental spectra. For that purpose LIFBASEis used, due to its ability to adjust the populations of the individual vibrational and rotational levels,thus enabling a full simulation of the laser pumping for the Q1(8) transition. The same procedure asfor the flame spectra is followed.

The process was iterative, changing several significant parameters until satisfactory agreement ofthe synthetic and experimental spectra was obtained. The controlling parameter was the R2 value,where R2 is the coefficient of determination. The maximum value of R2 corresponds to the optimumvalues of the fitting parameters and thus, of the spectral match. First, the rotational distribution withinv′ = 1 was varied for a certain temperature until the simulated spectrum was judged to be in the bestagreement with the experimental one, with the R2 as the controlling parameter. The majority ofthe population was placed in the laser pumped rotational level, N′ = 8, while the rest of the rotationallevels were left to follow Boltzmann distribution, thus defining a temperature. Second, the partitioningbetween the F1 and F2 spin components had to be varied as well. The fitting was started by keepingall the population in the excited spin orbit level (v′ = 1, F1 in this case). However, F2 needs to beincluded to improve the fit (generally adding about 20-30% population in that spin orbit, dependingon the LIF image section). For the fully thermalised case at 2000 K, the percentage of F1 and F2 is54.7% and 45.3%, respectively. Third, the distribution of the vibrational levels was adjusted, placingthe majority of the population in the v′ = 1 vibrational level. The population of the vibrational levelswas varied and adjusted, and the whole procedure repeated until the optimum spectral agreement wasachieved. The described fitting procedure was done for a range of temperatures, with the highestoverall value of R2 corresponding to the rotational temperature in the experiment, for that specificsection of the LIF image. The same analysis was further done for all 10 sections of a LIF image.Thus, the temperature distribution throughout the scramjet combustor width is obtained at the laserposition in the experiments. From Figure 6.15 it is evident that there is a unique peak R2 value whichcan be used to derive temperature. The uncertainty of the derived temperature was then assumed tobe the temperature resolution at which the LIFBASE spectra were generated at. For the example inFigure 6.15 the derived temperature is 1700±100 K.

In Figure 6.12 fits for several temperature values are compared to the experimental spectra. Fig-ure 6.13 shows the best fit achieved with the fitting process. It is evident that this fitted syntheticspectra is in significantly better agreement with the experimental spectra than the initial thermalisedsynthetic spectra in Figure 6.11. Figure 6.14 shows the corresponding rotational distribution for the


best fit, while the related change of R2 values for a temperature range is shown in Figure 6.15. Thisdistribution is dominated by the initially pumped level Q1(8) but shows that RET has occurred onlypartially. For the spectrum of section 2 of test # 11607 in Figure 6.13, about 20% of the total v′ = 1population is found in N′ = 8, and the remaining 80% is distributed among other levels in a roughly1700 K Boltzmann distribution, however, about 78% of the total population is retained within the F1component even when RET has taken place. This approach assumes that the rotational levels sur-rounding N′ = 8 have already equilibrated and thus follow a Boltzmann population distribution. Theagreement between the experimental and synthetic spectra is not perfect, and the disagreement can beattributed to several factors. First, the LIFBASE may not perfectly simulate the real effects. For ex-ample, it was impossible to simulate the region around 313 - 314.5 nm to perfectly fit the experiment.This issue is attributed to the modelling implemented in the LIFBASE software. Second, there areseveral parameters varied in the fitting procedure, making the process more complex. Third, factorslike rotationally dependent quenching and residual polarization effects might be affecting the results(Luque, 2016). However, despite these issues, the resulting temperature values are consistent with theexpected temperature values in scramjet combustor. Figure 6.16 shows an example of the obtainedtemperature distribution in the scramjet combustor, achieved for the experiment # 11607.

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ScramjetLIFBASE best fit

Figure 6.12: Experimental spectrum fitting to LIFBASE spectrum. Each LIFBASE spectrum is a fit at differenttemperature value. All spectra normalized to the same area.

In the Figure 6.17, the temperature distribution in the combustor is presented for several tunnel runs,i.e., several experiments in the test facility. One can observe that there are a few experimental datapoints where the temperature is significantly different from the remaining results, indicating that thesetemperature results might be erroneous. This was also observed by Neuber et al. (1996), where themuch higher values of temperature were explained as being biased due to insufficient concentrationof OH in the particular locations of the measurement volume. The present results are consistent


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Figure 6.13: Scramjet experiment spectrum fitted to LIFBASE spectrum. Spectra normalized to the same area.

0 5 10 15 20

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Figure 6.14: Rotational population distribution for section # 2 test # 11607.


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Figure 6.15: Coefficient of determination R2 for section # 2 test # 11607.

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Figure 6.16: Temperature distribution in thermal compression scramjet.


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Figure 6.17: Comparison of temperature distribution in thermal compression scramjet for different tests.

with their findings and raw LIF images show very low concentration of OH for the locations wheretemperature values have a high variation. Figure 6.18 shows spectra for two such data points, thefirst one for section 7 of test 11608 and second one for section 10 of test 11621. It is clear from thecomparison that these experimental spectra of low intensity differs significantly from the theoreticalspectra and thus results in an erroneous temperature value. Thus, it is justified that these data pointswere removed from the temperature distribution data set and all further analysis.

The t-distribution was used to give uncertainty of the presented results (Gosset, 1908). For a smallsample data set such as the temperature distribution presented, the value of standard deviation can beweighted to approximate the difference between finite and infinite statistical estimates. The larger thedata set, the more the weighted distribution resembles a normal distribution. Using a t-estimator, tn,the measurement is presented as

xi = x± tnσ (6.2)

For a sample of 7 measurements, tn = 2.365 for a two-sided distribution with 95% confidence interval(Figliola and Beasley, 2014). Figure 6.19 includes the average temperature, Tav, for the LIF temper-ature results with t-distribution applied. The largest error is in the sections near the combustor wallsand on the centre line, which is not unexpected considering the observed lower signal intensity levelin those regions.


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Figure 6.18: Example of spectra with low intensity signal. Spectra normalized to the same area. Sections withthese spectra were excluded from the temperature distribution as temperature considered erroneous.


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Figure 6.19: Comparison of temperature distribution in thermal compression scramjet for different tests.

The thermal compression scramjet temperature distribution was compared with the computationalfluid dynamics results of Bricalli (2015) with the US3D solver in Figure 6.20. In the high-compressionregion there is reasonable agreement between the experiments and CFD, with CFD temperature 3.5%lower than Tav at 33.75 mm and 24.13% lower at 3.75 mm. However, there is a significant discrepancyin the low-compression region, where CFD temperature is 26.21% lower than Tav at 41.25 mm and44.99% lower at 71.25 mm. The CFD results show no signs of combustion occurring in the low-compression region, and the temperatures of approximately 1100 K in that region are a result ofaerodynamic compression in the engine. LIF experimental results, on the contrary, due to the presenceof OH show that combustion is actually in process. Figure 6.21 shows pressure distribution for allLIF tests included in this research. In this figure top plot corresponds to the left, middle plot to thecentre and bottom plot to the right of the combustor, i.e., to the low compression, centre and highcompression region of the combustor, respectively. The pressure distribution for the low compressionregion (top plot) are concurrent with the temperature results. At the position of the laser at 0.307 mthe pressure values are an indication of combustion, while CFD pressure data of noticeably lowervalues do not indicate combustion. Therefore, CFD results used for comparison do not seem to beadequate or a true representation of the combustion in the used scramjet.


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Figure 6.20: Comparison of temperature distribution in thermal compression scramjet with CFD. The solidline shows Tav.


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Figure 6.21: Pressure data for LIF tests. From the top: low compression, centre and high compression regionof the combustor.


6.2 OH Emission Spectroscopy Measurements

Spectrally resolved OH emission measurements were taken at the same location as that done forthe LIF thermometry experiments. The slit location is at 0.307 m measured from the start of thecombustor. Figure 6.22 shows an example spectrum for the whole image. The same approach wasapplied as with the LIF experiments and the combustor was split into ten sections. An example of thespectrum in one section is shown in In Figure 6.23 , and the spectra for all ten sections are shown inFigure 6.24.

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Figure 6.22: Example of emission spectra for the whole image.

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Figure 6.23: Example of emission spectrum in a section.

Section 6.2 OH Emission Spectroscopy Measurements 98

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Figure 6.24: Emission spectra in all 10 sections.

The comparison of the emission results was made with the synthetic spectra of LIFBASE, SPARTANand Photaura. A good match with the result of Photaura’s optically thick case was obtained, like forthe third slit location in Figure 3.3. This is expected, as the location of the current measurements issimilar to the location of the third slit in the previous study (Brieschenk et al., 2013; Lorrain et al.,2013). Likewise, the difference that exists between optically thin and optically thick conditions canalso be observed in the present study. For the results in Figure 6.25 and Figure 6.26, the optically thinresults of LIFBASE and SPARTAN show a large discrepancy with the experimental results of thisstudy. This indicates that these emission spectroscopy experiments correspond to an optically thickflow. In Figure 6.27, experimental spectra is compared with the synthetic spectra of different opticalthickness. From this comparison it appears that the best agreement of emission experimental spectrais with the synthetic spectra with ∆ L = 0.1 m. This finding has no ramifications on the previous LIFresults obtained with non-thermal analysis, where fitting was done assuming optically thin flow. Thereason for this is that, even though the optical thickness affects the absorption (the laser beam isattenuated as it propagates down through the flow), this does not affect the presented temperaturemeasurements as the procedure to obtain temperatures only looks at a comparative intensity. It ispostulated that the 0 -0 band fluorescence may be affected by optical thickness. Figure 6.11 showsthat significantly more fluorescence is expected in the 0 - 0 band than is absorbed. There are twopossible explanations:

• Collisional repopulation rates from v′ = 1 to v′ = 0 are slow

• The v′ = 0 level is populated but the fluorescence is attenuated along the path that the lighttravels exiting the duct.


However, the 1 - 1 fluorescence will not be affected by optical thickness as the population in the lowerlevel v′′ = 1 at these temperatures is low. Thus, as temperatures in this work were determined byfluorescence that is almost all 1 - 1 band fluorescence, the assumption of optically thin flow in theanalysis was appropriate and there are no ramifications for the presented temperature distributionsobtained via LIF thermometry.

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LIFBASESPARTAN


Figure 6.25: Comparison of synthetic spectra at 3000 K with experimental results for the whole area.

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Figure 6.26: Comparison of synthetic spectrum at 3000 K with experimental results for a section.

Section 6.3 OH PLIF imaging considerations 100

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∆L=0.001m

Figure 6.27: Comparison of experimental results for one section with synthetic spectra for different pathlengths ∆ L.

6.3 OH PLIF imaging considerations

For the majority of LIF experiments the spectrometer was focused on the 300 - 320 nm spectral region.However, for several experiments this was changed and the spectrometer was focused at 360 nm. Thischange has brought some unexpected results. A strong fluorescence line was detected with intensityconsiderably stronger than the OH lines in the 300 - 320 nm spectral region, as shown in Figure 6.28.

This line does not look like an artefact, and the fact that this one line is much stronger than the othersin the OH spectrum can be an indication that:

• this line is connected to the laser-excited OH bands

• a line of another species is accidentally excited together with the OH Q1(8) line.

In order to investigate this phenomenon several approaches were tried:

• Repeating the same experiment but using different excitation lines. If another species line isexcited with Q1(8), then LIF images using different OH excitation lines should not show thisline around 360 nm.

• A nitrogen test. OH is an intermediate species in combustion process and using nitrogen as testgas suppresses combustion. So if this line is an OH line, it should not show in nitrogen test.

• PLIF tests with different excitation lines. Ideally, if this line is from another species and ac-cidentally excited together with Q1(8), then PLIF images using different OH excitation linesshould show different amount of fluorescence.


Figure 6.28: LIF image at 360 nm, for Q1(8).

Figure 6.29 shows that excitation with several different OH lines does not bring about the samefluorescence line around 360 nm as the excitation with Q1(8). In Figure 6.30, it is evident that thestrong line is present in a nitrogen experiment, indicating that this line is not an OH line, but a line ofanother species. Finally, Figure 6.31 shows PLIF images done with different OH excitation lines. Inthe case these images showed a greater fluorescence with Q1(8) than with other transition lines, thena conclusion could be made that the greater fluorescence signal with Q1(8) excitation is due to theanother species fluorescence as a result of the accidental simultaneous line excitation together withQ1(8) line excitation. Unfortunately, not much difference was observed in these PLIF images.

Investigation of the other elements with absorption lines around 283 nm has resulted in the findingthat the accidentally excited line of another species is most likely the one of iron, Fe I. There are infact two Fe I lines very close to the Q1(8), the stronger one at 283.62901 nm (Kramida et al., 2017).Also, Fe I has a strong line at 363.24981 nm, which corresponds to the experiment and shown inFigure 6.32. These two lines share the same upper energy level, which confirms that the iron line thathas been excited accidentally with Q1(8) and the one that was recorded around 363 nm are connected.Data in the Table 6.2 (Kramida et al., 2017) provides information on the two mentioned iron spectrallines.

Table 6.2: Iron (Fe I) energy levels

Wavelength [nm] Ei [cm−1] Ek [cm−1] Upper level (Config., Term, J)

283.55862 0.000 35257.324 3d7(4F)4p z5G 4

363.24981 7728.060 35257.324 3d7(4F)4p z5G 4


Figure 6.29: LIF images at 360 nm, for different excitation lines.

Iron contamination has been reported in the shock tubes (Park, 1993; Schneider and Park, 1975;Sharma and Park, 1990), shock tunnels (Palma et al., 1993) and expansion tunnels (McIntyre et al.,1998). Palma et al. (1993) measured the absolute emission intensities of the free piston shock tunnelflow, where elements such as iron, chromium, nickel, molybdenum, copper, tin and aluminium wereidentified. They postulated that these were produced by the erosion from the interior surfaces of theshock tunnel and heated by the flow. One method to reduce the impurities is to line the interior ofthe shock tube with copper. This removes the metallic impurities eroded from the shock tube wallsat the expense of the few strong copper lines. Sharma and Park (1990) found a high level of ironimpurities in the electric arc-driven shock tube experiments. Schneider and Park (1975) observed thesame kind of metallic impurities even when cold (without electric arc discharge) helium was usedas the driver gas in the experiments. Their finding indicated that these impurities originate at leastpartially from the shock tube material, stainless steel. Sharma and Park (1990) successfully avoidedthe iron contamination by the use of aluminium shock tube. Another study (Camm and Rose, 1962)performed in the aluminium shock tube found no discernible traces of iron impurities.

In this study it is postulated that like in the experiments of Palma et al. (1993) the erosion of the shocktunnel walls introduced iron particles in the flow that were accidentally excited with the laser whenexciting OH.


Figure 6.30: LIF images at 360 nm, for Q1(8) and nitrogen as test gas.

Even though PLIF images are not entirely conclusive, Figure 6.29 and Figure 6.30 show enoughevidence that this line is a line of another species excited when exciting Q1(8). Comparison of Fig-ure 6.32 with the known spectral lines brought to the conclusion that this species is iron, Fe I.

In the LIF experiments it is not important if the iron line is excited together with OH as the spectrom-eter is focusing on a certain spectral area. However, in PLIF experiments, where all the wavelengthsare observed at once, this finding plays a major role. Exciting two lines of two different species meansthat fluorescence of two origins is observed in PLIF images and it is not possible to make a distinc-tion between the fluorescence coming from OH and the one coming from another species. Therefore,these kind of results are ambiguous. A way to circumvent this is to use a filter that would block out allthe fluorescence coming from this iron line. As Q1(8) has been used quite frequently as the excitationline in PLIF studies, it is very important to make sure to avoid this in future and use another OHexcitation line for PLIF experiments.

Naturally, this is relevant only in the facilities built from an iron-based material, such as steel. Asprevious studies Camm and Rose (1962); Sharma and Park (1990) have shown, facilities built froman alternative material like aluminium will not have the iron contamination issue.


Figure 6.31: PLIF images for different excitation lines.


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Figure 6.32: LIF spectrum at 360 nm.

6.4 Summary

The main focus of this research was to obtain single-shot temperature measurements in a scramjetcombustor using thermally-assisted LIF. Experimental data was obtained through laser-induced fluo-rescence where a laser beam was focused into the combustor and the OH Q1(8) transition was excited.

Comparison of the experimental spectra showed there is a significant departure of the experimentalresults from thermal equilibrium simulations. The conclusion was that the OH conentrations in theLIF experiments is thermalised only to some extent and not fully. Therefore, the same approach wasfollowed as for the flame experiments and non-equilibrium spectral simulations were used. Thesenon-equilibrium LIFBASE spectra were fitted to the scramjet LIF emission spectra, thus obtaining atemperature distribution across the combustor width. The same analysis was done for several experi-ments in the test facility for which a good LIF signal was recorded.

The thermal compression scramjet temperature distribution was compared with the computationalfluid dynamics results of Bricalli (2015). The comparison showed a reasonable agreement betweenthe experiments and CFD for one side of the scramjet, while the other side showed a significantdiscrepancy between the data. As both LIF and pressure experimental data indicated combustion inthis region, while CFD results showed no combustion occurrence, the CFD results were found to beinadequate representation of the combustion in the used scramjet.

The comparison of the emission results was made with the synthetic spectra of LIFBASE, SPARTANand Photaura. A good match with the result of Photaura’s optically thick case was obtained.

Section 6.4 Summary 106

Measurements in the 360 nm spectral region resulted in detection of a strong fluorescence line. Inves-tigation of this phenomena led to the conclusion that when the Q1(8) OH line is chosen for excitation,another line of a different species that lies very close to Q1(8) is also unintentionally excited. It isbelieved that the second species is iron, Fe I. The assumption is that the erosion of the shock tunnelwalls introduced iron in the flow that is excited with the laser when exciting OH. Thus, it is very im-portant to make sure to avoid this in future and use another OH excitation line for PLIF experimentswhere iron may potentially also be present in the flow. Alternatively, fluorescence from this iron linecan be circumvented by proper filtering of the PLIF fluorescence.

Chapter 7

Modelling of the LIF process

One of the major issues associated with the quantitative interpretation of LIF experiments is thecompetition of the fluorescence emission with collision processes, as illustrated in the Chapter 2.Even though several alternatives of the LIF technique (i.e., saturated and predissociative LIF) aresufficiently insensitive to collisions for many combustion situations, no method is suitable for ev-ery application. Usually, detailed information on the efficiency of collisional energy transfer andits dependence on temperature and chemical composition of the environment is required for accu-rate measurements of temperature and concentration. This can result in difficulties with quantitativeinstantaneous LIF measurements in turbulent combustion conditions, as temperature and chemicalcomposition which determine the local non-radiative decay rate of a laser-excited state can vary sig-nificantly throughout the area of observation. Detailed numerical models which simulate all radiativeand collisional processes of relevance with the appropriate system of differential equations were de-veloped for analysis of the influence of energy transfer processes on the fluorescence signal. Thismodelling can also assist in the design of an experimental approach which is best suited for obtainingtemperature assuming levels are thermally populated from laser excited state.

7.1 Energy level models

The fundamental LIF technique consists of laser excitation from a particular vibrational-rotationallevel in the ground electronic state of the molecule to a particular vibrational-rotational level in anupper electronic state. Vibrational and rotational energy exchange collisions in the upper electronicstate populate other vibrational and rotational levels not populated by laser excitation. Spontaneousemission and quenching collisions reduce the number of molecules in the excited state after elec-tronic excitation by causing transitions to vibrational and rotational levels in the ground electronicstate. Collisional exchange in the ground electronic state, RET and VET cause redistribution of thepopulation over the rotational and vibrational ensemble of energy levels, respectively.

Section 7.1 Energy level models 108

To obtain the species concentration or temperature, the fluorescence from vibrational-rotational levelsin the upper electronic state is recorded and analysed. Analytical expressions relating measured fluo-rescence intensities to molecular species number density are utilized in a variety of models describingthe processes in LIF. The need to accurately simulate the energy transfer dynamics following laserexcitation has motivated the development of several computer models. These numerical models arebased on the description of the time dependent population in each energy level with a set of OrdinaryDifferential Equations (ODEs), called rate equations. Each ODE contains contributions to the energytransfer into or out of the respective level. The dimension of the system of ODEs is equal to thenumber of relevant energy levels.

The simplest way to illustrate single-photon LIF detection is a two energy level model (Figure 7.1).This model is mathematically simple and able to illustrate basic principles. It is applicable to LIFdetection of certain atomic species and molecular systems under specific conditions. These conditionsinclude either fully frozen or fully equilibrated rotational level manifolds. The limit where rotationalrelaxation is frozen (very low pressures) represents situations with no transfer to adjacent rotationallevels. In the fully equilibrated rotational relaxation (i.e., completely relaxed), the rotational transferis so fast that a Boltzmann distribution is rapidly established among the rotational levels. These thetwo energy levels can then be used to represent the two vibrational levels containing the rotationalmanifolds.

1

2

W12 W21 A21 Q12 Q21

Qion

Qpre

Figure 7.1: Two energy level diagram.

However, most of the real LIF processes lie somewhere in between these two borderline cases androtational energy transfer must be accounted for. This yields the four energy level model, first intro-duced by Berg and Shackleford (1979). Levels 1 and 2 in this model are particular rotational levels

Chapter 7 Modelling of the LIF process 109

that are connected through the absorption of the incident laser radiation and stimulated emission,while “levels” 3 and 4 represent groups or manifolds of rotational levels in the upper and lower elec-tronic state, respectively. In Figure 7.2 the absorption/spontaneous emission rate constant is given asW = B ·ρ , where B is the Einstein coefficient for absorption/stimulated emission and ρν is the laserspectral energy density. The downward rate constant T represents the sum of spontaneous emission,A, and quenching, Q, rate constants T = A + Q.

1

2

W12 W21 T21

3

4

T34

R23

R32

R14

R41

T24

T31

Figure 7.2: Four energy level model.

7.2 60-level rate equation model

The four-level model, however, does not include any effects of vibrational relaxation. For the broad-band detection used in the present study which encompasses two different vibrational bands in thedetection range, this model is thus not sufficient. Therefore a full vibrational-rotational level rateequation model was developed. This model includes a sequence of collision processes consisting of:level-specific excitation → RET within v′ = 1 → VET to v′ = 0 → RET within v′ = 0. Molecules inthe laser-coupled overpopulated vibrational level are transferred into other vibrational levels due tovibrational exchange collisions. Levels in the ground electronic state are populated by both sponta-neous emission and quenching from the upper electronic state energy levels. It is the relative strengthof these two sets of effects, one depleting the laser-coupled level and one populating the lower elec-tronic state level, which determines the extent of deviation from the ideal two-level model.

The model developed here is an extension of the four-level model, adding another vibrational level inthe upper electronic state. Thus, it includes two vibrational levels in the upper electronic state (v′ = 1

Section 7.2 60-level rate equation model 110

1

2

W12 W21 T21

3

4

T34

R23

R32

R14

R41

T24

T31

5

V25

V52

T51

V53V35

T54

Figure 7.3: Five energy level model.

and v′ = 0) and one in the ground electronic state (v′′ = 0). This would essentially make it a five-levelenergy model. However, to include the rotational relaxation effects each vibrational level is modelledto contain twenty rotational levels, the model thus yielding sixty energy levels in total. The timehistory of the population distribution in the sixty levels is found by solving the set of rate equations(ODEs) using the linear multi-step method of Gear.

dN1

dt=−N1W12 laser absorption

−N1 ∑m

R14m depleting RET

+N2W21 laser− stimulated emission

+N2T21 quenching and spontaneous emission

+∑i

N3iT31i quenching and spontaneous emission

+∑m

N4mR41m populating RET

+∑j

N5 jT51 j quenching and spontaneous emission

(7.1)


dN2

dt= N1W12 laser absorption

−N2W21 laser− stimulated emission

−N2T21 quenching and spontaneous emission

−N2 ∑m

T24m quenching and spontaneous emission

−N2 ∑i

R23i depleting RET

−N2 ∑j

V25 j depleting V ET

+∑i

N3iR32i populating RET

+∑j

N5 jV52 j populating V ET

(7.2)

dN3i

dt= N2R23i populating RET

−N3iT31i quenching and spontaneous emission

−N3i ∑i

T34i quenching and spontaneous emission

−N3iR32i depleting RET

−N3i ∑i

R3i depleting RET

−N3i ∑j

V35 j depleting V ET

+N3i ∑i

R3i populating RET

+∑j

N5 jV53 j populating V ET

(7.3)

dN4m

dt= N1R14m populating RET

−N4mR41m depleting RET

−N4m ∑m

R4m depleting RET

+N2T24m quenching and spontaneous emission

+∑i

N3iT34i quenching and spontaneous emission

+∑j

N5 jT54 j quenching and spontaneous emission

+∑m

N4mR4m populating RET

(7.4)


dN5 j

dt= N2V25 j populating V ET

+N3iV35 j populating V ET

−N5 jT51 j quenching and spontaneous emission

−N5 j ∑j

T54 j quenching and spontaneous emission

−N5 jV53 j depleting V ET

−N5 jV52 j depleting V ET

−N5 j ∑j

R5 j depleting RET

+∑N5 jR5 j populating RET

(7.5)

Starting conditions for the numerical simulations were: t = 0 s, T = 2300 K1, p = 1 atm, a Boltzmannpopulation distribution for the named conditions in the ground electronic state and zero populationin the upper electronic level. The total number of molecules is NT = 1000. Note that the use of theBoltzmann factor is based on the existence of equilibrium prior to and not during laser irradiation.Simulations were done for each section of the LIF image (Figure 6.3), like the fitting proceduredescribed in Chapter 6. In the simulations the temperature for a particular section was taken as thetemperature that was obtained for that section with the fitting procedure.

All energy transfer rate constants (Q, R, V , A) are assumed to be independent of temperature and initialrotational level. The respective efficiencies of these rates are strongly dependent on the collisionalpartners (i.e. chemical composition of the bath gas), collision frequency (i.e. pressure), and thevelocity of collision partners (i.e. temperature).

For the respective collision processes different modelling approaches can be used. Lengel and Crosley(1978) found that for rotational relaxation of OH near room temperature, the probabilities of transferto neighbouring rotational levels were approximately constant for a few levels and then decreasedrapidly. Hence, in modelling the rotational relaxation process, it was here assumed that each rotationallevel is directly connected via RET with five upper and five lower rotational levels within the samevibrational level. Downward rotational energy transfer is equally probable to any of the five rotationallevels closest to a particular level, while the probability of transfer past those levels is zero. The initialvalue for downward RET, R = 0.17 Rtot , was taken from Lucht et al. (1980).

1This temperature was obtained with the fitting procedure for the section taken for comparison.


R [Ju(i),Ju(k)] = 0.17Rtot , i f 0 < Ju(i)− Ju(k)≤ 5

R [Ju(i),Ju(k)] = 0, i f Ju(i)− Jl(m)≥ 5

Upward rotational relaxation rate constants are calculated by the principle of detailed balancing:

R [Ju(k),Ju(i)] = R [Ju(i),Ju(k)] · [gu(i)/gu(k)] · exp[Eu(k)−Eu(i)]/kBT (7.6)

The challenge with including the quenching rate constants for specific collision partners (H20, N2,CO, CO2, H2, etc.) in the rate equations is that the chemical composition must be known. This meansthat the concentration of dominant collision partners at the temperature at each measurement locationin the experiment must be either measured by a separate method or calculated in another way. Ingeneral, this is a very difficult requirement to fulfil, and as it was not possible in the present study,only a total quenching rate constant involving all (unknown) collision partners was used. At flametemperatures Jeffries et al. (1988) found that the quenching rate constant variation with rotationallevel is significantly smaller than the decrease of the quenching rate constant with increase of therotational level found by Copeland and Crosley (1984). Therefore, the electronic quenching fromany upper rotational level “i” or “j” is assumed to be equally probable (a flat quenching rate constantdistribution) to each of the lower rotational levels “m”:

Q [Ju(i),Jl(m)] = Qtot/40

Spontaneous emission, which is a much weaker process than electronic quenching at atmosphericpressure and above, is modelled as:

A [Ju(i),Jl(m)] = Aul, i f Ju(i) = Jl(m)

A [Ju(i),Jl(m)] = 0, i f Ju(i) 6= Jl(m)

Under typical flame conditions, VET is a slower process than both RET and quenching. HenceVET is generally both preceded and followed by RET. The experimentally detectable population in aparticular vibrational-rotational level is the net result of many different possible sequences of energylevel changing collisions, with various paths leading from the initially laser-populated level to the OHenergy level whose fluorescence is finally observed.


Like for quenching, the VET rate constants were assumed to be independent of the specific collisionpartner and only a total VET rate constant is used. This model assumes no rotational state change(∆J′ = 0) in transfer to the v′ = 0, but it does involve subsequent change in rotational level withinthe v′ = 0. In a study done by Campbell (1984b), the use of a flat distribution (equal probabilityto all levels) of final rotational levels after a VET exchange collision instead of standard ∆J′ = 0assumption made very little difference to the results. It was also assumed that there was no rotationallevel dependence on VET rate constants. The dependence of VET rate constants on the rotationallevel measured by Crosley (1981) showed a variation in the VET rate constant of about a factor of 2over 1 - 15 levels in the v′ = 1 at flame temperatures, which is too small to make a significant differencein the computational results.

In the upper A2Σ electronic level, the upward v′ = 0 to v′ = 1 VET rate constant is usually about an orderof magnitude lower than the downward v′ = 1 to v′ = 0 VET rate constant. The reason for this is as fol-lows: for the A2Σ electronic state of OH, the characteristic vibrational temperature is θv = 5133 K. Thismakes the exothermic v′ = 1 to v′ = 0 vibrational collisional exchange at the temperature T = 2000 Khighly favoured over the endothermic v′ = 0 to v′ = 1 exchange (Campbell, 1984a). Also, for standardconditions (T = 2000 K) the v′ = 1 to v′ = 0 VET rate constant was found to be approximately 0.6×Q.

During the development of this rate model, transfer rate constants were varied, the resulting pop-ulation was put into LIFBASE and synthetic spectra obtained with LIFBASE simulation was thencompared with the experimental spectra for one section. Figure 7.4 to Figure 7.7 correspond to thebest fit of the rate model spectra with the experimental spectra at T = 2300 K and the constants inTable 7.1. Firstly, the time evolution of population for certain levels is presented, while the best fit isshown later in Figure 7.13.

Table 7.1: Comparison of total transfer rate constants.

Total transfer rate constants [s−1]

A Q R V (1→0) V (0→1)

This study (eg.) 1·107 1·109 1·1010 0.7·108 0.35·108

Lucht et al. (1980) 1·107 1·109 1·1010 - -

Levels 1 and 2 are directly coupled by laser absorption, where molecules are pumped by the laserfrom lower level 1 to higher level 2. This can be seen in the Figure 7.4 showing the time evolutionof population in levels 1 and 2. During the laser pulse the population of level 1 is reduced, returningto equilibrium state shortly after the pulse. In contrary, the population of level 2 increases from zeroto the same value taken from the population of level 1, and after the laser pulse it quickly returns tozero, i.e., to its equilibrium state. The time required for both levels to return to their equilibrium stateafter the laser pulse is approximately 20 ns.


Figure 7.5 shows the population evolution in levels neighbouring level 2 (N′ = 8 in v′ = 1) that arepopulated predominantly by RET from level 2, but also by RET from their adjacent levels. The levelsthat are closer to the laser pumped level 2 (levels 37 and 39) have higher population than levels furtherfrom the level 2 (levels 36 and 310). All levels in this Figure show the same qualitative behaviouras level 2, increasing from zero to a certain level, and shortly after the laser pulse returning to theirequilibrium state. The same qualitative behaviour is observed for the levels in Figure 7.6, whichshows the population evolution in manifold 5. These rotational levels are populated predominantly byVET from the level 2 (58), and levels 37 (57) and 39 (59), and are by smaller amount populated by RETfrom their adjacent levels. Level 58 populated predominantly by VET from the laser excited level 2has higher population than levels populated by levels not excited by laser. In general, the populationin levels of manifold 5 is approximately an order of magnitude smaller than the population in levelsof manifold 3. This is consequence of VET = 0.7·108 [s−1], which is predominant mode of transferto manifold 5 from manifold 3, being smaller than RET = 0.5·109 [s−1] between levels of manifold 5.Time evolution of population for each of 60 rotational levels in this model, for T = 2300 K is includedin the Appendix D.

Figure 7.7 represents an example of rotational distributions in vibrational levels v′ = 0, 1 and v′′ = 0for ∆ t = 300 ns (same as the time interval during which LIF measurements were taken). Boltzmanncurve was plotted with each of the rotational distributions for comparison. These distributions show:

• v′ = 1: the directly excited level 8 is clearly overpopulated, while the remaining levels followapproximately a Boltzmann distribution. There is a slight deviation from a fully Boltzmanndistribution in the levels adjacent to the excited level.

• v′ = 0: with the exception of rotational level 8, the population follows approximately a Boltz-mann distribution.

• v′′ = 0: the population distribution in this vibrational level is a Boltzmann distribution.

These distributions provide support to the validity of the approach followed in the temperature fittingprocedure presented in Chapter 6, i.e., assumption of Boltzmann distribution in v′ = 1 for all levelsexcept the laser coupled levels, and a Boltzmann distribution in v′ = 0, was correct. Thus, the use offitting procedure to deduce rotational temperature as described in Chapter 6 is validated.

As the temperature is obtained from the fluorescence recordings which are a result of fluorescenceemission from the upper electronic state, the focus here is on v′ = 0, 1. The starting temperaturefor numerical simulation of a particular section is the temperature for that section obtained withthe fitting procedure and it has proven to yield the best agreement with the experimental spectrawhen the other temperature values were tried for the simulation (Figure 7.8). There is not muchdifference between the spectra at different temperatures, however, based on the small differences


50

80

50 300

Pop

ulat

ion

Time [ns]

Level 1

0

15

30

50 300

Pop

ulat

ion

Time [ns]

Level 2

Figure 7.4: Example of population evolution in levels 1 and 2 for ∆ t = 300 ns.

between results of fitting procedure at different temperatures shown in Figure 6.12, this finding wasexpected. A greater difference between different rate model spectra is seen in Figure 7.9, showing thespectra obtained with different R values, in comparison with the experimental spectra. Note that thisis downward R, upward rates are always obtained with detailed balancing that includes downward R

(Equation 7.6). Even for small variations of R there is difference between the spectra. Figure 7.10shows the sensitivity in variation of the vibrational transfer rate constant from the v′ = 1 to v′ = 0, V

(1→0). There is quite a bit of sensitivity observed for this rate constant, and small variations producenoticeable difference in the resulting spectra. Naturally, the greatest difference here is observed inthe intensity levels of VET populated v′ = 0. Noticeable difference was also seen for the variation ofquenching rate constant, Q, shown in Figure 7.11. Compared to Figure 7.10, more difference here isobserved in the intensities of laser-coupled levels, and much less for the thermally populated levels.


The least sensitivity, thus least difference in the resulting spectra, was observed for variation in thevalue of V (0→1), as shown in Figure 7.12.

Figure 7.13 represents the comparison of spectra for a particular section from the scramjet experimentwith the best fit spectra for the same section obtained with the rate model. This rate model spectrawas obtained through acquiring the energy level populations with the rate model as stated earlier, andputting those population numbers into LIFBASE which is then able to simulate the spectra shown inFigure 7.13.

7.2.1 Alternative case

The results and comparisons shown so far are all considering a particular section of a LIF image.When another LIF image section is used for comparison, rate model parameters have to be changedin order for the numerical spectra be in agreement with the experimental spectra. This is logical as LIFimage is obtained across the width of the combustor and different sections of the image correspondto different sections of the combustor, i.e., different experimental conditions. The relevant conditionsare primarily temperature and chemical composition, both influencing collision rate constants, thusthe rate model requires changing in the form of appropriately altered constants. Figure 7.14 shows thecomparison of another LIF image section spectra with the corresponding best fit rate model spectra.The most interesting finding here is that in order to achieve good agreement only temperature valuehad to be changed in the rate model (Table 7.2). This is not surprising as transfer rates are nottemperature dependent in the model, only upward R obtained through detailed balancing.

Table 7.2: Comparison of level transfer rate constants.

Level transfer rate constants [s−1]

Q R V (1→0) V (0→1)

This study (eg.#1) 109/40 0.2·109 0.7·108 0.35·108

This study (eg.#2) 109/40 0.2·109 0.7·108 0.35·108

Lucht et al. (1980) 109/20 0.17·1010 - -


0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 36

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 37

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 39

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 310

Figure 7.5: Example of population evolution in levels of manifold 3 for ∆ t = 300 ns.


0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 57

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 58

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 59

Figure 7.6: Example of population evolution in levels of manifold 5 for ∆ t = 300 ns.


0 5 10 15 20

Rot

atio

nal p

opul

atio

n

Rotational level

v'=1

Boltzmann curve

0 5 10 15 20

Rot

atio

nal p

opul

atio

n

Rotational level

v'=0

Boltzmann curve

0 5 10 15 20

Rot

atio

nal p

opul

atio

n

Rotational level

v''=0

Boltzmann curve

Figure 7.7: Example of rotational distribution in vibrational levels v′ = 0, 1 and v′′ = 0 for ∆ t = 300 ns.


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

306 308 310 312 314 316 318 320

Spe

ctra

l int

ensi

ty, I

λ [a

rbitr

ary

units

]

Wavelength [nm]

Scramjet experimentRate model T=2300KRate model T=2200KRate model T=2000KRate model T=1700KRate model T=2500K

Figure 7.8: Comparison of scramjet experiment and rate model spectra for different temperatures.Spectra normalized to the same area.

0

0.1

0.2

0.3

0.4

0.5

0.6

306 308 310 312 314 316 318 320

Spe

ctra

l int

ensi

ty, I

λ [a

rbitr

ary

units

]

Wavelength [nm]

Scramjet experimentRate model R=0.015RtotRate model R=0.017RtotRate model R=0.020RtotRate model R=0.025Rtot

Figure 7.9: Comparison of scramjet experiment and rate model spectra for different R.Spectra normalized to the same area.


0

0.1

0.2

0.3

0.4

0.5

0.6

306 308 310 312 314 316 318 320

Spe

ctra

l int

ensi

ty, I

λ [a

rbitr

ary

units

]

Wavelength [nm]

Scramjet experimentRate model V10=0.35*108

Rate model V10=0.7*108


Rate model V10=1*108

Figure 7.10: Comparison of scramjet experiment and rate model spectra for different V (1→0).Spectra normalized to the same area.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

306 308 310 312 314 316 318 320

Spe

ctra

l int

ensi

ty, I

λ [a

rbitr

ary

units

]

Wavelength [nm]

Scramjet experimentRate model Q=1*109

Rate model Q=1.1*108



Figure 7.11: Comparison of scramjet experiment and rate model spectra for different Q.Spectra normalized to the same area.


0

0.1

0.2

0.3

0.4

0.5

0.6

306 308 310 312 314 316 318 320

Spe

ctra

l int

ensi

ty, I

λ [a

rbitr

ary

units

]

Wavelength [nm]

Scramjet experimentRate model V01=0.35*108



Rate model V01=1*108

Figure 7.12: Comparison of scramjet experiment and rate model spectra for different V (0→1).Spectra normalized to the same area.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

306 308 310 312 314 316 318 320

Spe

ctra

l int

ensi

ty, I

λ [a

rbitr

ary

units

]

Wavelength [nm]

Scramjet experimentRate model T=2300K

Figure 7.13: Comparison of scramjet experiment and rate model spectra. Spectra normalized to the same area.


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

306 308 310 312 314 316 318 320

Spe

ctra

l int

ensi

ty, I

λ [a

rbitr

ary

units

]

Wavelength [nm]

Scramjet experimentRate model T=1700K

Figure 7.14: Comparison of scramjet experiment and rate model spectra. Spectra normalized to the same area.


7.3 Summary

Detailed numerical modelling which simulates all radiative and collisional processes of relevance withthe appropriate system of differential equations is required to accurately calculate the temperatureand total molecular concentration from the observed fluorescence signal. Such numerical modelling,especially for the unsteady-state case, requires accurate knowledge on electronic quenching as well asinformation on vibrational and rotational energy transfer (VET and RET, respectively). Calculationsof this type are necessary for analysis of the influence of energy transfer processes on the fluorescencesignal. Thus, a detailed numerical model which simulates all radiative and collisional processes ofrelevance with the appropriate system of differential equations was developed for analysis of theinfluence of energy transfer processes on the fluorescence signal. This modelling can also assist inthe design of an experimental approach which is best suited for a specific combustion scheme. Theachieved population distributions demonstrated that the approach followed in the fitting procedure,i.e., assumption of Boltzmann distribution in v′ = 1 for all levels except the laser coupled levels, and aBoltzmann distribution in v′ = 0, was correct. This validates the use of the fitting procedure to deducerotational temperature as described in Chapter 6.

Chapter 8

Conclusions and recommendations for futureresearch

The research presented in this thesis provides a significant contribution to scramjet research, because,to the author’s knowledge, this is the first time thermally-assisted LIF was used for for scramjet flows.In addition, this study represents successful single-shot scramjet temperature measurements. Theavailability of a thermometry technique that provides temperature from a single run of a test facility isespecially appealing considering the significant per-shot cost of running high enthalpy facilities. Fur-thermore, scramjet supersonic combustion is an extremely unsteady phenomenon. Thus, in such anenvironment obtaining a temperature from each experiment appears more accurate than the commonapproach where results of several experimental runs are averaged to get temperature. The outcome ofthe project brings new resources which can be further used in advancing the technology of operationalscramjet engines for hypersonic vehicles.

The project was approached theoretically (synthetic spectra), experimentally and numerically (CFDand LIF modelling). The results of all three aspects were compared to deduce the accuracy andreliability of the experimental results and the experimental technique.

• Radiation simulation programs providing synthetic OH spectra represent the theoretical partof this study, as they employ theoretical expressions for spectral calculations. Three differentcodes include OH species - LIFBASE, SPARTAN and an in-house program Photaura. All threeprograms give correct and reliable representation of the physical phenomena in the wavelengthrange studied.

• Experimental data was obtained through laser-induced fluorescence where a laser beam wasfocused into the combustor and an OH molecule transition (A2 Σ+; v′ = 1 - X2 Π; v′′ = 0) wasexcited. The experimental campaign was conducted in the T4 shock tunnel using a 3D scramjetmodel. The laser-induced fluorescence measurements were performed to resolve temperatures

Chapter 8 Conclusions and recommendations for future research 127

in the combustor region. The OH radical is an intermediate species in the chemical process ofcombustion, created in high quantities, allowing therefore direct fluorescence measurements.

• The numerical aspect presented in the project are the results of Bricalli (2015), in the form of thecomputational fluid dynamics (CFD) simulations of the combustion process, which provided uswith the indication of the phenomena occurring in the flow studied. Additionally, these resultspresented a valuable comparison to experimental temperature distribution.

• Detailed numerical modelling which simulates all radiative and collisional processes of rele-vance with the appropriate system of differential equations is required to accurately calculatethe temperature and total molecular concentration from the observed fluorescence signal. Suchnumerical modelling, especially for the unsteady-state case, requires accurate knowledge onelectronic quenching as well as information on vibrational and rotational energy transfer (VETand RET, respectively). Calculations of this type are necessary for analysis of the influence ofenergy transfer processes on the fluorescence signal. Thus, a detailed numerical model whichsimulates all radiative and collisional processes of relevance with the appropriate system ofdifferential equations was developed for analysis of the influence of energy transfer processeson the fluorescence signal. This modelling can also assist in the design of an experimentalapproach which is best suited for a specific combustion scheme.

8.1 Conclusions

Spectral modelling

The numerical codes SPARTAN and Photaura were modified in order to include the hydroxyl radical.The results of the SPARTAN and Photaura spectral simulations were then compared with the resultsof the LIFBASE simulation that already contains OH in its database. The results presented in thisthesis show that OH spectra produced using these programs show very good agreement. There areseveral reasons for the slight discrepancies between the three programs. First, the source codes havedifferent radiation modelling. Calculation of parameters that influence the spectra are performed indifferent ways resulting in discrepancies observed between the three spectra. Second, even thoughmost of the spectroscopic constants are the same in both SPARTAN and Photaura input files, eachof these codes still uses some specialised inputs as well. This can produce some discrepancies insimulation results.

In addition, a comparison was made with the experimental results of an inlet-injection supersoniccombustion study (Brieschenk et al., 2013; Lorrain, 2014). Each slit location result was comparedwith all three synthetic spectra corresponding to the optically thin flow. The observed differencebetween experimental and synthetic spectra, increasing with the increase in the wavelength, is an

Section 8.1 Conclusions 128

indication that the experiments show a departure from the optically thin case, and that in reality eventhe first slit location, at the combustor entrance, doesn’t correspond to the ideal case of opticallythin flow. These experimental results were therefore further compared with the optically thick flowsimulations, calculating optical thickness for each case separately. A good match with the result ofPhotaura’s optically thick case was obtained, with optical thickness varying between slit locationsand being the greatest for the third slit location at the end of the combustor. The reason for furtherdiscrepancies could be the spectral signature of other species radiating in the same wavelength (suchas CH). Also, the origin of the discrepancies might be the imperfection of the numerical programsresulting in the small differences when results are compared with the experimental results.

Flame LIF thermometry

The LIF setup was tested and calibrated with atmospheric H2 flame experiments. The comparisonwith thermalised spectral simulation results showed that the experimental spectral is thermalised onlypartially. Thus, a non-equilibrium spectral simulation was used in order to have a proper comparisonand a possibility of a better agreement with the experimental spectra. By fitting the LIFBASE spectrato the flame experimental spectra, a very good agreement of the synthetic and experimental spectrawas achieved. The best fit corresponds to the optimum values of the fitting parameters and thus,of the spectral agreement. The main fitting parameters were temperature, species concentration andspin-orbit combination factor (the partitioning between the F1 and F2 spin components). The fittingwas done for a range of temperatures, and the best fit used to find the rotational temperature in theexperiment, for that specific section of the LIF image. The analysis was repeated for all of the 10sections of a LIF image. Thus, the temperature distribution throughout the flame was obtained at thelaser position in the experiments. The temperature distributions along the flame height were obtainedfor two positions within the flame and two excitation lines (Q1(8) and Q1(9)). There were somediscrepancies between the results for different excitation lines, possibly due to differences in LIFsignal recorded.

An interesting phenomenon was found during the analysis of the flame results : the described fittingprocedure was possible only for the results obtained when the excitation line was a Q line, irrelevantof the J-number. It was not possible to achieve the same results when the fitting method was appliedto the LIF data where excitation was by a R line. The reason for this remained unclear, however it isimportant to note it when choosing an excitation line for the future experiments, whether in a flameor in a scramjet. When the excitation was by a P line, the fitting was essentially possible, however theresults were considered erroneous due to low signal, i.e., insufficient OH present in the measurementvolume, and therefore were excluded from comparison with Q line fitting results.

These results were verified with the temperature profile obtained with the well-established multi-line thermometry approach. The comparison shows good agreement between these two thermometry


techniques. The discrepancies may be attributed to the differences between the synthetic spectra con-stants and the experimental ones, the multi-parameter fitting and differences between the thermometrymethods approach.

Scramjet LIF thermometry

The main focus of this research was to obtain single-shot temperature measurements in a scramjetcombustor using thermally-assisted LIF. Given the environment in which these experiments wereperformed (turbulent, supersonic combustion and LIF data is time-resolved within few nanoseconds),the most accurate approach is to analyse data from each tunnel run separately.

The laser-induced fluorescence spectra was compared with the thermal equilibrium simulations. Thecomparison showed there is a significant discrepancy between these spectra and that the experimentalOH concentrations were only partially thermalised. Thus, the same approach was followed as for theflame experiments and non-equilibrium spectral simulations were used. The scramjet broadband LIFemission spectra was evaluated with a full spectral fit and temperature distribution along combustorwidth was obtained. This was done for several experiments in the test facility for which a good LIFsignal was recorded.

Comparing these temperature distributions it was observed that for a few experimental data pointsnear the combustor wall the temperature was diverging from the remaining results, indicating thatthese temperature results might be erroneous. Neuber et al. (1996) observed this in their study andthey explained the much higher values of temperature as being biased due to localized insufficientconcentration of OH. This work’s results are consistent with their findings and raw LIF images showedvery low concentration of OH for the combustor locations where temperature values have a highvariation. These data points were removed from the temperature distribution data set and all furtheranalysis.

To give uncertainty of the presented results, a t-distribution was used (Gosset, 1908). The largestobserved error was in the sections near the combustor walls and on the centre line, which is notunexpected considering the observed lower signal intensity level in those regions.

The thermal compression scramjet temperature distribution was compared with the computationalfluid dynamics results of Bricalli (2015). In the high-compression region there was a reasonableagreement between the experiments and CFD. However, the low-compression region showed a sig-nificant discrepancy between the data. The CFD results show no signs of combustion occurring inthat area, and the temperature is the indication of compression only. LIF experimental results, on thecontrary, show that the combustion is actually in process. Pressure distribution for that region wereconcurrent with the temperature results showing that combustion was occurring. At the position ofthe laser the pressure values indicated combustion, while the CFD pressure data of noticeably lower

Section 8.1 Conclusions 130

values do not indicate combustion occurrence. Therefore, CFD results used for comparison do notseem to be an adequate or a true representation of the combustion in the used scramjet.

LIF modelling

A detailed numerical model which simulates all radiative and collisional processes of relevance withthe appropriate system of differential equations was developed for analysis of the influence of energytransfer processes on the fluorescence signal. This modelling can also assist in the design of an ex-perimental approach which is best suited for a specific combustion scheme. The achieved populationdistributions proved that the approach followed in the fitting procedure, i.e., assumption of approx-imately Boltzmann distribution in v′ = 1 and a Boltzmann distribution in v′ = 0, was correct. This isvalidates the use of the fitting procedure to deduce rotational temperature as described in Chapter 6.

Scramjet emission

The comparison of the emission results was made with the synthetic spectra of LIFBASE, SPARTANand Photaura. A good match with the result of Photaura’s optically thick case was obtained. Thiswas expected, as the location of this studies experiments is similar to the location in previous study(Brieschenk et al., 2013; Lorrain et al., 2013). Likewise, the difference that exists between opticallythin and optically thick conditions was also observed in the present study. It was further shown thatthe optically thin results of LIFBASE and SPARTAN show a large discrepancy with the experimentalresults of this study. This demonstrated that the scramjet combustion experiments correspond to theoptically thick flow.

Scramjet PLIF

Measurements in the 360 nm spectral region revealed some unexpected results. A strong fluorescenceline was detected with intensity considerably stronger than the OH lines in the 300 - 320 nm spectralarea. Investigation of this phenomena led to the conclusion that when the Q1(8) OH line is chosenfor excitation, another line of a different species that lies very close to Q1(8) is also unintentionallyexcited. It is believed that the second species is iron, Fe I. It is a well known fact that shock tunnelexperiments have a high level of driver gas contamination (Boyce et al., 2005; Stalker and Crane,1978), however, iron contamination has not been reported previously in the test gas. In this study it isassumed that the erosion of the shock tunnel walls introduced iron in the flow that is excited with thelaser when exciting OH.

In the LIF experiments conducted here, it is not important if the iron line is excited together withOH, as the spectrometer is filters out the iron fluorescence. However, in PLIF experiments, whichare not spectrally resolved and where all the wavelengths are observed at once, this finding can play


a major role. Exciting two lines of two different species means that fluorescence from two originsmay be observed in PLIF images and it is not possible to make a distinction between the fluorescencecoming from OH and the fluorescence coming from another species. Therefore, these kinds of resultsare ambiguous, unless careful filtering is employed. As Q1(8) has been used quite frequently as theexcitation line in PLIF studies, it is very important to make sure to avoid this in future and use anotherOH excitation line for PLIF experiments where iron may potentially also be present in the flow.

8.2 Recommendations for Future Research

The experimental results of this research present some interesting possibilities for future experiments.Some recommendations for future work are presented here.

An improvement to the experimental equipment would be a flat flame burner (McKenna burner) withwhich it would be possible to better characterize flame experiments.

The scramjet used in this study is an engine based on the thermal compression concept. Thermalcompression is a method that takes advantage of the scramjet engine flow non-uniformities to en-courage combustion throughout the entire flow. Spanwise regions of locally high temperature andpressure (high compression regions) are produced which ignite the air-fuel mixture. This results inhigh combustion efficiencies achieved with a reduced risk of engine choking. However, it means thatthe flow within the engine is an extremely complex three-dimensional flow. Thus, it is more difficultto accurately simulate with CFD. This thesis presented a comparison with CFD results, and the con-clusion was that the previous CFD results were incorrect in simulating combustion in the scramjet.Therefore, it is proposed that the same LIF thermometry experiments are done in a simpler two-dimensional engine, for which CFD simulations would have a higher chance of correctly resolvingthe flow features.

The thermometry method used has shown good results in this study where the OH molecule wasprobed. It would be interesting to try the same approach in different conditions, for example targetingNO molecules in a facility nozzle exit. This would be another way of validating this thermometrymethod.

The temperature distribution along the combustor width was obtained in this work. A step furtherwould be to add another dimension - a second laser beam perpendicular to the first one to get lon-gitudinal temperature distribution. Each tunnel run would then provide two times one-dimensionaltemperature distribution and thus deeper insight into the combustion. This would be beneficial inunderstanding the combustion process within the scramjet.

The fluorescence signal in the present scramjet experiments was captured during a 300 ns exposuretime, including the time during the laser pulse. It would be good to repeat the experiments capturing

Section 8.2 Recommendations for Future Research 132

fluorescence only after the laser pulse, and compare the results. It is expected that by capturing thefluorescence after the pulse only, the spectra would be fully in thermal equilibrium.

For flame experiments, a comparison of the temperature results obtained by fitting were comparedwith the temperature obtained through multi-line thermometry. It would be valuable for the validationof this thermometry method if the same would be done with the scramjet data. This would mean doingscramjet experiments with different excitation lines that have sufficient energy spacing, which wouldallow the temperature to be found from the multi-line Boltzmann plot.

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Appendix A

Spectroscopic constants: OH-G.txt

S p e c t r a l _ C o n s t a n t s _ L e v e l s _ A 2 S _&_X2P_ ( Luque&Cros l ey_1998 )

Level_A

3 .268E+04 3 .178E+03 −9.268E+01 −1.773E+00 3 .079E−01 −3.459E−02 0 .000E+001 .739E+01 −8.581E−01 2 .453E−02 1 .745E−02 −1.385E−02 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00

0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00

0 .201 0 .196 0 .192 0 .193 gammaA

Level_X

0 .000E+00 3 .738E+03 −8.491E+01 5 .584E−01 −2.597E−02 −0.639E−03 1 .340E−051 .890E+01 −7.250E−01 8 .329E−03 −9.502E−04 8 .041E−06 −5.866E−06 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00 0 .000E+00

−4.200E−06 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+000 .000E+00 0 .000E+00 0 .000E+00

−138.92017 −0.265359 −0.004987 0 .001393 AX

99 N u c l e a r _ S p i n _ S t a t i s t i c a l _ W e i g h t

1 e x p l i c i t _ v a l u e s

Level_A ( v )10 N u m b e r _ v i b r a t i o n a l _ l e v e l s0 1 2 3 4 5 6 7 8 9

V i b r a t i o n a l _ l e v e l s10 N u m b e r _ v a r i a b l e s1 2 3 4 5 6 11 8 9 10 V a r i a b l e s _ c o d e

nu0A_BvA_mDvA_HvA_LvA_MvA_AvA_gammaA_34250 .1166 16 .96506 −2.063218 e−3 1 .22990 e−7 0 .13729 e−10 −0.3651 e−14 0

Spectroscopic constants: OH-G.txt 146

37238 .6866 16 .129332 −2.045047 e−3 1 .01114 e−7 0 .05890 e−10 −1.3320 e−14 040031 .7866 15 .286447 −2.04786 e−3 0 .92210 e−7 0 .44940 e−10 0 042625 .3366 14 .42222 −2.06501 e−3 0 .01600 e−7 0 0 045010 .9566 13 .5172 −2.138e−3 0 0 0 047173 .3908 12 .543 −2.41e−3 0 0 0 049089 .3728 11 .4302 −2.701e−3 0 0 0 050713 .8508 10 .117 −4.26e−3 8 .50000 e−6 0 0 051987 .6578 8 .3399 −4.71e−3 −2.93000 e−6 0 0 052825 .2728 5 .9744 −7.27e−3 −32.4000 e−6 0 0 0

gammaJA_gammaJJA_LIFBASe0 .22555 −4.77e−5 0 . 7 6 e−80 .2161 −4.62e−5 1 . 0 5 e−80 .2066 −4.39e−5 0 . 7 0 e−80 .1975 −3.30e−5 0 . 7 0 e−80 .178 0 00 .161 0 00 .144 0 00 .128 0 00 .1557 0 00 .1889 0 0

Level_X ( v )11 N u m b e r _ v i b r a t i o n a l _ l e v e l s0 1 2 3 4 5 6 7 8 9 10

V i b r a t i o n a l _ l e v e l s10 N u m b e r _ v a r i a b l e s1 2 3 4 5 6 11 8 9 10 V a r i a b l e s _ c o d e

nu0X_BvX_mDvX_HvX_LvX_MvX_AvX_1847 .7366 18 .53487379 −1.908974 e−3 1 .42915 e−7 1 .5167 e−11 12 .58 e−16 −139.05088415418 .0908 17 .82391653 −1.870453 e−3 1 .37917 e−7 1 .616 e−11 17 .46 e−16 −139.3205088822 .8310 17 .12246166 −1.835718 e−3 1 .31700 e−7 1 .693 e−11 18 .82 e−16 −139.58693

12063 .8860 16 .4278983 −1.805889 e−3 1 .2422 e−7 1 .797 e−11 1 9 . 3 e−16 −139.8441415142 .3466 15 .7370 −1.7825 e−3 1 .154 e−7 1 . 8 8 e−11 1 9 . 5 e−16 −140.08218058 .3226 15 .0455 −1.7668 e−3 1 .054 e−7 1 . 9 8 e−11 1 9 . 5 e−16 −140.29220810 .6916 14 .34855 −1.7674 e−3 0 .9418 e−7 2 . 0 8 e−11 1 9 . 5 e−16 −140.43023396 .8306 13 .63950 −1.7715 e−3 0 .8136 e−7 2 . 1 8 e−11 1 9 . 5 e−16 −140.50025812 .3776 12 .908903 −1.80091 e−3 0 .336 e−7 2 . 3 e−11 1 9 . 5 e−16 −140.4305728050 .1838 12 .145252 −1.85734 e−3 −0.184e−7 2 . 4 e−11 1 9 . 5 e−16 −140.1410730100 .2768 11 .332467 −1.9547 e−3 −0.986e−7 2 . 5 e−11 1 9 . 5 e−16 −139.5059

gammaX_gammaJX_gammaJJX_LIFBASe−0.1191965 2 .326 e−5 0 .265 e−8−0.1137661 2 .304 e−5 0 . 3 5 e−8−0.108189 2 .245 e−5 0−0.102482 2 .264 e−5 0−0.0965 2 . 4 7 e−5 0−0.0906 1 . 1 6 e−5 0−0.0838 2 . 0 0 e−5 0−0.0737 2 . 8 4 e−5 0−0.06687 3 . 4 8 e−5 0−0.05513 4 . 1 5 e−5 0−0.04077 6 . 5 0 e−5 0

0 P e r t u r b a t i o n s

100 R o t a t i o n a l _ L e v e l s8 V i b r a t i o n a l _ L e v e l s

999 999 999 999 999 999 999 999 JEmax_TO_BE_IMPLEMENTED999 999 999 999 999 999 999 999 JGmax_TO_BE_IMPLEMENTED

Franck_Condon_Fac to r s_ ( Luque&Cros l ey_1998 )

9 .049 e−01 9 .167 e−02 3 .300 e−03 5 .190 e−05 2 .930 e−07 0 .000 e−00 0 .000 e−00 0 .000 e−008 .712 e−02 7 .086 e−01 1 .915 e−01 1 .280 e−02 3 .300 e−04 3 .700 e−06 0 .000 e−00 0 .000 e−007 .190 e−03 1 .711 e−01 4 .985 e−01 2 .891 e−01 3 .272 e−02 1 .350 e−03 0 .000 e−00 0 .000 e−006 .400 e−04 2 .490 e−02 2 .377 e−01 2 .947 e−01 3 .586 e−01 6 .856 e−02 4 .440 e−03 0 .000 e−006 .600 e−05 3 .190 e−03 5 .313 e−02 2 .695 e−01 1 .329 e−01 4 .074 e−01 1 .213 e−01 1 .203 e−020 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00

Spectroscopic constants: OH-G.txt 147

0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−000 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00 0 .000 e−00

E i n s t e i n _ C o e f f i c i e n t s _ A _ ( LIFBASE )

1 .451 e +06 6 .387 e +03 1 .924 e +02 1 .079 e +01 3 .753 e−03 1 .348 e−02 5 .215 e−03 7 .096 e−044 .606 e +05 8 .678 e +05 7 .421 e +03 8 .181 e +02 6 .877 e +01 7 .883 e−02 2 .363 e−02 7 .798 e−038 .983 e +04 6 .838 e +05 4 .568 e +05 4 .789 e +03 2 .305 e +03 2 .450 e +02 9 .735 e−01 5 .610 e−021 .542 e +04 2 .331 e +05 6 .931 e +05 1 .980 e +05 1 .604 e +03 5 .056 e +03 7 .039 e +02 8 .248 e +002 .679 e +03 6 .157 e +04 3 .797 e +05 5 .592 e +05 6 .650 e +04 4 .731 e +01 9 .766 e +03 1 .677 e +034 .656 e +02 1 .452 e +04 1 .402 e +05 4 .484 e +05 3 .476 e +05 1 .385 e +04 6 .016 e +02 1 .638 e +048 .489 e +01 3 .470 e +03 4 .517 e +04 2 .252 e +05 3 .948 e +05 1 .400 e +05 1 .071 e +03 1 .246 e +031 .688 e +01 9 .147 e +02 1 .462 e +04 9 .574 e +04 2 .589 e +05 2 .169 e +05 2 .349 e +04 2 .345 e +02

Appendix B

Spectroscopic constants: OH-LEV.txt

2 L e v e l s1 N u c l e a r _ S p i n _ D e g e n e r a c y

S t a t e Mode Te we Be a l p h a D0 geX 0 0 3737 .794 18 .896 0 .7250 35593 2A 0 32684 .1 3178 .86 17 .389 0 .858 18956 2

Appendix C

Spectroscopic constants per vibrational level

Spectroscopic constants per vibrational level 150

Tabl

eC

.1:V

ibra

tiona

lly-s

peci

ficco

nsta

nts

[cm−

1 ]for

the

X2 Π

grou

ndle

veli

nL

IFB

ASE

.

v=0

v=1

v=2

v=3

v=4

v=5

v=6

v=7

v=8

v=9

v=10

T 0el

ectr

onic

ener

gy0a

3570

.354

269

75.0

9941

a10

216.

1494

4a13

294.

61b

1621

0.58

6189

62.9

5521

549.

094

2396

4.64

1b26

202.

4472

b 2825

2.54

02b

Bro

tatio

nco

nsta

nt18

.534

8737

9a17

.823

9165

3a17

.122

4616

6a16

.427

8983

a15

.737

b15

.045

514

.348

55b

13.6

395b

12.9

0890

3b12

.145

252b

11.3

3246

7b

Dx1

04fir

stce

ntri

fuga

ldis

tort

ion

cons

tant

19.0

8974

a18

.704

53a

18.3

5718

a18

.058

89a

17.8

2517

.668

17.6

74b

17.7

1518

.009

1b18

.573

4b19

.547

b

Hx1

08se

cond

cent

rifu

gald

isto

rtio

nco

nsta

nt14

.291

5a13

.791

7a13

.17a

12.4

22a

11.5

410

.54

9.41

8.13

63.

36b

-1.8

4b-0

.986

b

Lx1

012th

ird

cent

rifu

gald

isto

rtio

nco

nsta

nt15

.156

7a16

.16a

16.9

3a17

.97a

18.8

19.8

20.8

21.8

23b

24b

25b

Mx1

016fo

rth

cent

rifu

gald

isto

rtio

nco

nsta

nt12

.58a

17.4

6a18

.82a

19.3

a19

.519

.519

.519

.519

.519

.519

.5A

spin

-orb

itco

uplin

gco

nsta

nt-1

39.0

5088

41-1

39.3

2050

8a-1

39.5

8693

a-1

39.8

4414

a-1

40.0

82b

-140

.292

-140

.43b

-140

.5b

-140

.430

57b

-140

.141

07b

-139

.505

9b

γsp

in-r

otat

ion

cons

tant

-0.1

1919

65-0

.113

7661

a-0

.108

189a

-0.1

0248

2a-0

.096

5-0

.090

6-0

.838

-0.7

37-0

.066

87b

-0.0

5513

b-0

.040

77b

γD

x104

-II-

0.23

26a

0.23

04a

0.22

45a

0.22

64a

0.24

7c0.

116c

0.2

0.28

4b0.

348b

0.41

5b0.

65b

γH

x108

-II-

0.26

5a

γLx1

012-I

I-0.

35a

0a0a

00

00

00

0p

λ-d

oubl

ing

cons

tant

0.23

5266

113a

0.22

4676

7a0.

2319

2528

a0.

2028

392a

0.19

12e

0.17

84e

0.17

07e

0.15

42d

0.13

635b

0.11

684b

0.09

273b

p Dx1

04-I

I--0

.517

115a

-0.5

1446

a-0

.515

31a

-0.4

994a

-0.5

133e

-0.5

123e

-0.5

113e

-0.5

103d

-0.5

123

-0.5

113b

-0.5

103

p Hx1

08-I

I-0.

4957

a0.

483a

0.48

a0.

473a

0.46

5b0.

46b

0.45

b0.

44d

0.43

b0.

42b

0.41

b

q-I

I--0

.038

6932

445a -0

.036

9394

38a -0

.035

1742

08a

-0.0

3338

788a

-0.0

3156

1e-0

.029

72e

-0.0

277e

-0.0

259d

-0.0

2354

d-0

.021

15b

-0.0

1849

8b

q Dx1

04-I

I-0.

1474

207a

0.14

473a

0.14

2277

a0.

1401

4a0.

1392

4e0.

1382

2e0.

1376

2e0.

1374

1d0.

1422

b0.

1433

7b0.

1411

1b

q Hx1

08-I

I--0

.272

20a

-0.2

6385

a-0

.251

97a

-0.2

429a

-0.2

29c

-0.2

2b-0

.21b

-0.2

b-0

.19b

-0.1

8b-0

.17b

aM

élen

etal

.(19

95)

bC

olin

etal

.(20

02)

cC

oxon

(198

0)d

Cop

elan

det

al.(

1993

)e

Cox

onan

dFo

ster

(198

1)

Spectroscopic constants per vibrational level 151

Tabl

eC

.2:V

ibra

tiona

lly-s

peci

ficco

nsta

nts

[cm−

1 ]for

the

A2 Σ

exci

ted

leve

lin

LIF

BA

SE.

v=0

v=1

v=2

v=3

v=4

v=5

v=6

v=7

v=8

v=9

T 0el

ectr

onic

ener

gy32

402.

383

5390

.95

3818

4.05

4077

7.6

4316

3.22

4532

5.65

4724

1.64

4886

6.11

5013

9.92

5097

7.53

6B

rota

tion

cons

tant

16.9

6506

c 16.1

2933

2c 15.2

8644

7c 14.4

222c 13

.517

2f

12.5

43f

11.4

302

f10

.117

f8.

3399

f5.

9744

f

Dx1

04fir

stce

ntri

fuga

ldis

tort

ion

cons

tant

20.6

3218

c20

.450

47c

20.4

786c

20.6

501c

21.3

8f

24.1

f27

.01

f42

.6f

47.1

f72

.7f

Hx1

08se

cond

cent

rifu

gald

isto

rtio

nco

nsta

nt12

.299

c10

.111

4c9.

221c

0.16

c0

00

850

f-2

93f

-324

f

Lx1

012th

ird

cent

rifu

gald

isto

rtio

nco

nsta

nt13

.729

c5.

89c

44.9

4c0c

00

00

00

Mx1

016fo

rth

cent

rifu

gald

isto

rtio

nco

nsta

nt-3

6.51

c-1

33.2

c0c

0c0

00

00

0A

spin

-orb

itco

uplin

gco

nsta

ntγ

spin

-rot

atio

nco

nsta

nt0.

2255

5c0.

2161

c0.

2066

c0.

1975

c0.

178

f0.

161

0.14

4f

0.12

8f

0.15

57f

0.18

89f

γD

x104

-II-

-0.4

77c

-0.4

62c

-0.4

39c

-0.3

3c0

00

00

0γ

Hx1

08-I

I-0.

76c

1.05

c0.

7c0.

7c

γLx1

012-I

I-0

00

00

00

00

0p

λ-d

oubl

ing

cons

tant

00

00

00

00

00

p Dx1

04-I

I-0

00

00

00

00

0p H

x108

-II-

00

00

00

00

00

q-I

I-0

00

00

00

00

0q D

x104

-II-

00

00

00

00

00

q Hx1

08-I

I-0

00

00

00

00

0

cC

oxon

(198

0)f

Cox

onet

al.(

1991

)

Appendix D

Rate model

Rate model 153

D.1 Manifold 3

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 30

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 31

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 32

Figure D.1: Example of population evolution in levels of manifold 3 for ∆ t = 300 ns.

Rate model 154

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 33

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 34

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 35

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 36


Rate model 155

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 37

0

15

30

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 2

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 39

Figure D.3: Example of population evolution in levels of manifold 3 for ∆ t = 300 ns.Level 2 is level 8 in the v′ = 1

Rate model 156

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 310

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 311

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 312

0

10

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 313


Rate model 157

0

5

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 314

0

5

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 315

0

5

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 316


Rate model 158

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 317

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 318

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 319


Rate model 159

D.2 Manifold 4

18

20

22

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 40

35

40

45

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 41

49

55

61

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 42


Rate model 160

58

68

78

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 43

66

77

88

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 44

70

80

90

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 45

70

80

90

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 46


Rate model 161

68

78

88

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 47

50

80

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 1

58

66

74

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 49

Figure D.9: Example of population evolution in levels of manifold 4 for ∆ t = 300 ns.Level 1 is level 8 in the v = 0

Rate model 162

50

57

64

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 410

44

49

54

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 411

37

40

44

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 412

31

33

35

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 413


Rate model 163

26.4

26.8

27.4

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 414

20.4

21

21.6

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 415

15

16

17

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 416


Rate model 164

10.8

12.2

13.5

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 417

7.5

9

10.5

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 418

5

6.7

8.4

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 419


Rate model 165

D.3 Manifold 5

0

0.5

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 50

0

0.5

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 51

0

0.5

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 52


Rate model 166

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 53

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 54

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 55

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 56


Rate model 167

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 510

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 511

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 512

0

1

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 513


Rate model 168

0

0.35

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 514

0

0.35

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 515

0

0.35

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 516


Rate model 169

0

0.15

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 517

0

0.15

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 518

0

0.15

50 300

Pop

ulat

ion

[num

ber

of m

olec

ules

]

Time [ns]

Level 519


temperature measurements in hypervelocity flows using

Documents